Finally got around to writing WWW::KeePassRest to solve this problem. And also wrote an article about the writing of the module, background stuff, etc.

To make a long story short, if you set things up in your KeePass database and install the KeePassRest plugin, you can do this:

   use LWP;
   use WWW::KeePassRest;
   use strict;
 
   my $url = 'http://somesite.com/aa/bb/cc.html';
   my $browser = LWP::UserAgent->new('Mozilla');
   $browser->credentials("somesite.com:80", "Realm",
      WWW:::KeePassRest->get_by_title('Some site credentials',
                                      'UserName', 'Password'));
   my $response=$browser->get($url);
[download]

And voila! You have secure password access. Like magic.