The idea is to refactor the portions of your code that can be shared by A.cgi and B.cgi. Consider the following:

my $data = 'pretend this is a complex data structure';
my $is_web_browser = 1;

if ($is_web_browser) {
    print qq(<span color="red">$data</span>\n);
}
else {
    print qq(\e[0;31m$data\e[0m\n);
}
[download]

file: SomeModule.pm

package SomeModule;
use strict;
use warnings;

sub get_data {
    return 'pretend this is a complex data structure';
}

1;
[download]

file: app.cgi

use strict;
use warnings;
use SomeModule;

my $data = SomeModule::get_data();
print qq(<span color="red">$data</span>\n);
[download]

file: app.pl

use strict;
use warnings;
use SomeModule;

my $data = SomeModule::get_data();
print qq(\e[0;31m$data\e[0m\n);
[download]

This is a very simple and distilled example, but hopefully you see how different apps can reuse the same modules without actually executing each other as a script.

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)