Somehow this problem is by design

but I wonder if there is a way to avoid this.

#!/usr/bin/perl
use NaServer qw(run);
run(@ARGV);
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And then do all the testing on NaServer::run instead. Since it's located in a module, you just use it once in the test script, apply the monkey patching you need, and just test as usual.

Other solution:

1) put a package YourPackage; in front of the string you eval, and after the run clean the namespace with an appropriate CPAN module

2) just as 1), but use a separate package name for each run, thus avoidng name collisions.

Thanks for the input which seems to have brought me a huge step forward. I did some tests and tries and following the code and my findings for future reference.

Since there was such a strong bias towards putting anything into a module, I tried your quiet radical way of

#!/usr/bin/perl
use NaServer qw(run);
run(@ARGV);
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First I had to rewrite my example, adopting it towards real-life in order to have something on which I can prove, that I can test what I want to test even if it is wrapped into module. The background was, that I wanted to write an integration-test, which takes some command-line arguments, feeds them to the tested script and checks, if the output is what I expect. Here comes the script-version, which is the common way of handling user-input but is hard to test.

Script Version

The test-stcript; the tested script is beneath the DATA-token. This code does not run, due to a redefinition of a sub_say. (At least not the testing-code, the tested script just runs fine.)

#!/usr/bin/perl -w
use warnings;
use strict;
use feature qw(switch say);
use English;

use Test::More  tests => 20; #'no_plan'; 
use Test::MockObject;
use Test::Output;
use Test::Trap;

my $mock = Test::MockObject->new();
$mock->fake_module ('NaServer', 
                new    => sub { return 'NaServer' },
                get_val  => sub { return 500 },
                );
use_ok( 'NaServer' )  or exit; ## includes 'use NaServer;' 

# Construction of $s just for testing
my $s = NaServer->new( 'sim8aXXXXXX', 1, 6 );
isa_ok( $s, 'NaServer');

# ==================================
# = Tests of the script start here =
# ==================================
use File::Slurp;
#my $script = 'script_to_test_with_subs.pl';  # used __DATA__ instead
my $code_to_test = do { local $/; <DATA> };
my @cases = ( 
                {   
                    name => 'wrong_threshold',
                    argv => 'hudriwudri',
                    expected_stdout => qr'invalid argument',
                    expected_stderr => '',
                    expected_exit => 3,
                },
                {
                    name => 'high_threshold',
                    argv => 1000,
                    expected_stdout => qr'OK',
                    expected_stderr => '',
                    expected_exit => 0,
                }    
            );
foreach my $case (@cases) {
    use_ok('NaServer');
    can_ok( 'NaServer', 'new');
    can_ok( 'NaServer', 'get_val');
    my @r = trap {  
        $ARGV[0] = $case->{'argv'};
        #eval read_file($script);
        eval $code_to_test; ## no critic (ProhibitStringyEval)
        if (defined $EVAL_ERROR) { die $EVAL_ERROR };
    };
    if ($trap->die) {
        croak $trap->die;
    }
    if ($trap->warn) {
        foreach (@{$trap->warn}) {
            warn $_ . "\n";
        }
    }
    like ( $trap->stdout, $case->{'expected_stdout'}, 
       "$case->{'name'}: stdout as expected" );
    is ( $trap->stderr, $case->{'expected_stderr'},
       "$case->{'name'}: stderr as expected" );
    is ( $trap->exit, $case->{'expected_exit'}, 
       "$case->{'name'}: exit-value as expected" );
}

__DATA__

# ==================
# = Script to Test =
# ==================

#!/usr/bin/perl -w
use warnings;
use strict;
use feature qw(switch say);
use NaServer;

my $threshold = $ARGV[0] || exit 3;
if ($threshold =~ /\d+/) {
    my $session = NaServer->new();
    my $val = $session->get_val();
    if ($val > $threshold ) {
        say_it ("Value to high: " . $val);
        exit 2;
    } else {
        say_it ("Value OK ($val)");
        exit 0;
    }
    
} else {
    say 'invalid argument';
    exit 3;
}

sub say_it {
    my $msg = shift;
    say $msg;
    return;
}
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Module-Version of the same logic and functionality.

As suggested by moritz I put all logic into a module. This should be easier to test.

Extension-Module (NaServerExt.pm, replacement for the "Script to Test" in the above example)

package NaServerExt;
# this is a wrapper around the *dummy version* of NaServer !!
use strict;
use warnings;
use feature qw( say );
use Carp;

use NaServer;

sub run {
    my ($self, @argv) = @_;
    my $threshold = $argv[0] || croak 'no arguments';
    if ($threshold =~ /\d+/) {
        my $session = NaServer->new();
        my $val = $session->get_val();
        if ($val > $threshold ) {
            _say_it ("Value to high: " . $val);
            exit 2;
        } else {
            _say_it ("Value OK ($val)");
            exit 0;
        }
    } else {
        say 'invalid argument';
        exit 3;
    }
}

sub _say_it {
    my $msg = shift;
    say $msg;
    return;
}
1;
__END__
=pod

=head1 USAGE

This module substitutes a script using NaServer.pm (the dummy-version 
+only!). 
This way it is easier to test.

It could be used by a script like this:

    #!/usr/bin/perl -w
    use warnings;
    use strict;
    use NaServerExt;

    NaServerExt->run(@ARGV);
    __END__

Do not forget: This is just for demonstrating something about testing 
+and has
nearly to nothing to do with NetApps NaServer modules!!

=cut
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Testscript (NaServerExt.t)

The above module allows to write a clean and relatively simple test, with mocking and various user-input simulated.

#!/usr/bin/perl -w
use warnings;
use strict;
use feature qw( say );
use English;

use Test::More  tests => 26; #'no_plan'; 
use Test::MockObject;
use Test::Output;
use Test::Trap;

my $mock = Test::MockObject->new();
$mock->fake_module ('NaServer', 
                new    => sub { return 'NaServer' },
                get_val  => sub { return 500 },
                );
use_ok( 'NaServer' )  or exit; ## includes 'use NaServer;' 

# Construction of $s just for testing
my $s = NaServer->new( 'sim8aXXXXXX', 1, 6 );
isa_ok( $s, 'NaServer');

# ==================================
# = Tests of the module start here =
# ==================================
my @cases = ( 
                {   
                    name => 'wrong_threshold',
                    argv => 'hudriwudri',
                    expected_stdout => qr'invalid argument',
                    expected_stderr => '',
                    expected_exit => 3,
                },
                {
                    name => 'high_threshold',
                    argv => 1000,
                    expected_stdout => qr'OK',
                    expected_stderr => '',
                    expected_exit => 0,
                },    
                {
                    name => 'low_threshold',
                    argv => 20,
                    expected_stdout => qr'Value\ to\ high',
                    expected_stderr => '',
                    expected_exit => 2,
                }    
            );
foreach my $case (@cases) {
    use_ok('NaServer');
    can_ok( 'NaServer', 'new');
    can_ok( 'NaServer', 'get_val');
    use_ok('NaServerExt');
    can_ok('NaServerExt', 'run');
    my @r = trap {  
        NaServerExt->run($case->{'argv'});
    };
    if ($trap->die) {
        croak $trap->die;
    }
    if ($trap->warn) {
        foreach (@{$trap->warn}) {
            warn $_ . "\n";
        }
    }
    like ( $trap->stdout, $case->{'expected_stdout'}, 
       "$case->{'name'}: stdout as expected" );
    is ( $trap->stderr, $case->{'expected_stderr'},
       "$case->{'name'}: stderr as expected" );
    is ( $trap->exit, $case->{'expected_exit'}, 
       "$case->{'name'}: exit-value as expected" );
}
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Conclusion

Since the radical approach of writing minimal scripts and several layers of modules makes the code easier to test, I will try to redesign the script in this direction. Thanks again!

Appendix

The NaServer.pm, if someone wants to play with the examples above:

package NaServer;
# this is just a dummy version of NetApps NaServer !!
use strict;
use warnings;
use Carp;

sub new {
    my $class = shift;
    my $self = {};
    bless \$self, $class;
}

sub get_val {
    return rand 1000;
}

1;
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or

write better scripts, write modules :)