• you can use modules from your own filesystem space setting the environment variable PERL5LIB to some path. This path will be prepended to perl's search path - see perlrun.
• certainly you can start hacking the HTTP::Proxy module, store the results in a path of your choice and use it, althogh I don't encourage it other than for your learning experience.
• here is a good choice to ask for advice, and visiting this site frequently will bring you enlightenment. I suggest you to use Super Search to find nodes on your topic.
• You claim that the source code of HTTP/Proxy.pm looks similar to your example, but alas, I cannot join you in that claim, for I do not have insight into your example. All I have is a script of yours, which proves LWP::UserAgent to be working fine.
• Post that example, so we can help you to work out how to get HTTP::Proxy work as expected.

regards,
--shmem

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}