How to attach a walking cane to a puppet

I would just include the cane as part of the arm. No need to get into magnets or anything special. You can still tag/rig the arm like normal, but just have cane artwork extending out from it. Making the cane independent and including a stick in it should help it stay rigid and prevent bending as well. 

As an example, Chief from https://okaysamurai.com/puppets/ has a coffee cup in one of this hands. Sirr on that page has a stick extention that can be triggered as well.