use strict;
use warnings;

package Package_One;

use vars qw( $VERSION );
#our $VERSION;

$VERSION = 'irrelevant';

# "our $VERSION" comes from the target module; without "our" there's no problem

my $eval =<<'END_EVAL';
    no strict;
    local $VERSION;
    $VERSION=undef; do {
      our $VERSION = 'desired_version';
    }; 
    $VERSION
END_EVAL

printf "Version: %s\n", Package_Two->_eval($eval);

package Package_Two;

sub _eval
{
    eval  $_[1];
}