Good timing on my part I suspect, but I just did this very thing last night. Unfortunately I wasn't paying full attention but I seem to have got it up and running. I used the CPAN shell, following all module dependencies. I'd also upgraded Bundle::CPAN just beforehand, though I don't know if that made a difference. There was a bit of a problem with the URI module - failed one of its heuristic tests (#6, for your reference). I just force-installed it (terribly irresponsible, I know. It will probably come back to bite me :-P). After that LWP breezed through. If this doesn't work for you, you may be missing some system libraries. Did you do a custom install of Slackware?. You could try building the modules by hand and make a note of anything it claims is missing.

Hope this is of some help. Perserverence is the key to Slackware :-)