Depends on your application. I would guess that (code) size of your own code should not be a problem (if you haven't developed it for years). It is either your data or the combined size of many CPAN-modules. Your own data you can minimize by removing global vars (if any), not having big arrays in memory, things you probably thought of yourself already.

CPAN modules are probably not built with memory efficiency in mind. You might be able to switch out modules with comparable functionality but smaller footprint or more importantly a smaller list of dependencies (or even replace them with your own code). But for that to work you should know the size of the cpan-modules you use. Something like perl -e 'use somemodule; while (1) {}' to check the size with 'ps' or 'top' might be sufficient to give you an idea of the base memory need of a module with dependencies. Better might be some test code with a typical use case

Some modules might have reserved space for caches. Check their documentation or their code