You don't have to have MIME::Lite installed in the system-wide paths, you can just install it in your user home directory and use lib ('/my/user/home'); to add that to your @INC path at runtime.
You can do that even without using CPAN.pm. Just download the tarball from CPAN, extract it, create the necessary directory structure in your user home directory (/home/me/MIME/ for example) and drop Lite.pm into it. You might also want MIME::Types and Mail::Address both of which are pure perl, and although it'll be faster at runtime with cpan::MIME::Base64 and MIME::QuotedPrint which both have bits of XS in them, it will get by just fine without them.
Spending a few minutes getting those things into place will be a lot faster than rolling your own MIME encoder.