is there a way to do the same sort of thing without if then statements?

You can use references to subroutines in a hash, then check if the key exists.
The following example does not do any real error checking, security, or check any return values, but it should help point you in the correct direction.

#!/usr/bin/perl -w

use strict;

print "Starting.\n\n";

my %actions = (
    'open'         => \&fileOpen,
    'create'    => \&fileCreate,
    'delete'    => \&Nono::fileDelete,
    'test'        => \&fileTest,
);


while ( <DATA> ) {
    chomp;
    next if /^\s*$/;
    my ( $function, $file ) = split( /\s+/, $_, 2);
    print "Testing '$function' -> '$file' . . .";
    exists( $actions{ $function } )
        ? &{$actions{ $function }}( $file )
        : print "\t'$function' does not exist\n";
}

print "Done.\n\n";
exit(0);

sub fileOpen {
    my $open = shift;
    ## open( BLAH, $open ) or die;
    ## actions
    ## close( BLAH );
    print "\tGot file '$open' to open.\n";
    return;
}

sub fileCreate {
    my $create = shift;
    ## open( BLAH, ">$create" ) or die;
    ## actions
    ## close( BLAH );
    print "\tGot file '$create' to create.\n";
    return;
}


package Nono;

sub fileDelete {
    my $delete = shift;
    ## actions
    print "\tGot file '$delete' to delete.\n";
    return;
}

package main;

sub fileTest {
    my $test = shift;
    ## actions
    print "\tGot file '$test' to test.\n";
    return;
}

__DATA__
open    line1
test    line2
create    line3
test    line 4 blah blah
delete    line5
open    line 6
nothing    line 7 fails
xxx    line8 fails too
fail    This will fail
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