Well, I understand your feelings about giving up and reinstall. But keep in mind that knoppix is
somewhat mixed and thats can make things hard to upgrade or install.

But then again. perl-doc is just docs, right?

You did try to download the deb file
and just do

dpkg --install perl-doc.deb

It seems not to try to resolve anything and I used this to install deborphan
without install get-text even it was listed as required. It still worked.

But its properly part of perlbase or something and not a single deb file but you might find it
on the net.

Well, good luck