If you stay within the typically installed and maintained modules for sites that use CPanel and bundle everything else in the libraries directory of your project (with appropriate adjustments to your use paths, of course) you should be fine for most other servers your target audience will use. Either they'll be on a CPanel or Plesk managed server or they'll have arrangements to do things themselves or to hire it done.

Typically, but not always, I distribute to my clients in two separate archive files. One is the project proper. The other is the dependencies, precompiled with a compatible perl, cc, processor, and OS if they are not pure-perl modules. I keep them separate from the system perl and usually separate from each other in case the projects depend on different interfaces in different versions of the same module. Deployment consists of uploading and extracting the project, and if that doesn't work, uploading and extracting the dependencies in the same folder. If I need anything outside the web root, I make sure the relative paths are saved in the archives.

If your customer are running something like perl 5.6.2 on Irix 6, then they'll know how to do all their own module installations. At least they should, or have access to someone who does.