There's no easy answer. You have a couple of options, though, and if this is intended to be a long-lived production server I strongly recommend giving all of these serious thought before choosing which one is right for you. Read around the subject both here at at the monastery and on the CentOS fora to get a feel for the pros and cons.

You could continue to use the system perl, use packaged modules where you can (eg. use the perl-Moose package to get Moose and all its dependencies) and only install those modules from source which are not available as packages. You must be very careful not to overwrite the system modules if you do this.

You could continue to use the system perl but set up your own personal library path and install all the modules required into that personal area from CPAN using an installer (cpan/cpanplus/cpanminus). This still takes a bit of care but you can do it all as a fairly unprivileged user which can help. Watch out for the contexts if you have SELinux enabled (which you should, of course).

Or you could go the whole hog, leaving the system perl well alone and installing a fresh perl of your own choosing elsewhere (from source) and then install the modules with that perl into its own dedicated library paths. This seems to be the option favoured by most monks here but I wear many hats and when wearing my sysadm hat am less keen on this as it becomes a hassle and therefore a danger at medium scales.

Whichever way you go, make a plan and stick to it. If it really does turn out to be the wrong choice it can be a bit of a nightmare to switch later. Good luck.