Weird they would let you install Perl but not additional modules.

It it is possible to repackage Perl yourself. A few years ago, I did that with StrawberryPerl.com (note .com not .org).

As I recall, I used the "PortableZIP edition". I unzipped it, ran the post-unzip scripts, "installed" needed CPAN modules, then zipped it into a new zip file.

It is also possible to create an MSI installer if you need to. I used nsis.sourceforge.net to create one. Unfortunately, I don't remember the details, but it wasn't hard to do.

I've never created an install package for Linux despite Linux being my primary platform, so I can't help you with that.

To expand on RonW's suggestion, here's one thought. Put portable Strawberry Perl on a USB drive stick. Use the portable Perl to install CPAN::Mini. Then make your own miniCPAN mirror on the same USB drive stick. Since Strawberry Perl already comes with App::cpanminus installed, it's then super easy to use cpanm to install any additional needed modules from your miniCPAN.

Going this route, you never "install" anything on your system. You run Perl from your USB stick. Or you can copy the portable Strawberry Perl from the USB stick to your system so that you don't have to rely on the USB stick all of the time.

And if you're trying to distribute something to coworkers, you can install PAR::Packer and then use pp to bundle your Perl script into a stand-alone executable. That way you won't have to worry about maintenance of Perl environements on everyone else's system. (Maintenance such as which version of Perl is installed, what modules are installed, what version of modules are installed, etc.)