Now, I'm a bit at a lost as to what to do next and was wondering if
anybody could offer suggestions for a web site, store, or whatever that
would attach my lump to the top of a walking stick.

I would start with a diamond drill bit to drill your glass lump (in a
drill press if possible), a bolt sunk into the stick (possibly a hanger
bolt), and some epoxy to hold the glass to the bolt.
All these things should be available at your local home center, or do a
google search.
Stay safe,
Andy