I avoid using the system perl, installing my own elsewhere. This also removes the issue of mixing and matching cpan and apt (or other package manager) module installs, which has issues of it's own. OS rolling out different versions of things, removing that control from me. I want to retain control of the software stack.

At work we have /app/productname I install perl, and the other dependencies. This means that I can simply transfer what I require from development into our other environments. I use a local cpan mirror created by minicpan as the basis for installation. All our servers are the same OS/Hardware.

cpan has the autobundle option, which you could use as a starting point for generating a single package for installing your dependencies. Take a look at the output and you'll see why I suggest only using it as a starting point.

12.04 & 16.04 ship with different versions of perl and you'll run into the binary compatibility issue if you try and copy modules which aren't pure perl.

If possible I'd suggest you consider starting fresh with a 16.04 server and start from scratch.

Update: Slight formatting change.