If the module (and all its dependencies) is pure perl then you could trivially bundle it with your application. CPANdeps has an option to tell you if stuff is pure-perl or not.
Otherwise if the admins won't allow you to just install stuff, take it up with your manager. If they are sensible you will need to be able to justify installing the extra software, but I'm sure you can do that. Things like "it will save development time", "it's well tested and here are the CPAN testers reports".
Remember, the sysadmins' job isn't to obstruct you (even if some of them can make it feel like it is), it's to provide and maintain the infrastructure that you and other parts of the business need.
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