“Hold on" is a phrasal verb with several different meanings, such as continue. "Hold onto" is the verb "hold" plus a preposition, and the preposition needs an object, like a cane. Thus, there are several possibilities, some of which are practically the same. (This is why phrasal verbs are difficult.) One could say "hold onto the cane" or "hold on to the cane". Same thing. I guess you could also say "hold on the cane", but that does not sound natural to me, though grammatically correct.