As you are on a shared host it is unlikely that you'd be able to take advantage of mod_perl or mod_proxy as suggested.
Take a look at LWP, specifically LWP::Simple. It should be easy to write a quick script something like this (not tested):
my $url = CGI->param('url');
print get( $url );
which would be called using something like: http://your.host.com/the_script.pl?url=http://google.com
This is primitive but should work for very basic things.
--tidiness is the memory loss of environmental mnemonics