generally speaking perl is perl wherever it runs, so you should be able to run your programs almost everywhere (there are OS specific but it is not your case). Strawberry can compile and install everything on cpan, so no incompatibilities.

Your question lacks of details and so answers cannot be more detailed.

The real problem is your old web application and if it is not too complex I suggest you to rewrite it using a modern perl web framework like Dancer2 or Mojolicious: a bit of effort to learn them but a great advantage for future maintainence and security.

Mojolicious has nice guides.

L*

Different Perl versions might confront you with deprecations, such that you'll need to fix the code. But Perl tends to be extremely backwards compatible.

You just need to test it.

edit

Probably trying different Perl versions in between to facilitate nailing down the deprecations.

I cannot supply an actual answer but I can let you know my experience of migrating from ActivePerl to Strawberry Perl.

No major issues at all!
Like you, I had planned and thought and worried...but in the end there were a few modules that needed updating which were easy to identify.

However, unlike you I am not running a web application on a Windows box. Instead, I migrated a number of standalone scripts and simple Tk applications. I seem to remember it was Tk that caused most of the few problems.