uses 10 modules

While you may be using only 10 modules directly, those modules use other modules (then these again may use other modules - you get the idea) so in reality your script may be loading dozens or even hundreds of modules under the hood.

For every module the Pi has to load the file and execute it.

So there are two reasons of slowness: The slowness of the Pi's CPU and the slowness of the SD-card as a storage medium.

To mitigate the CPU-slowness you could try to overclock the Pi (this is pretty safe), to mitigate the slowness of the card you could use a USB-stick or a USB hard-drive and set up your perl-environment in such a way that it loads the modules from there.

I fact you can even set up the Pi in such a way that it loads the whole OS from a USB-device (but you still need an SD-card for booting) which should also speed up the boot process.