To answer the explicit question,
Should we answer questions in multiple sections, describing different, but equally valid answers based on different tools or multiple answers, each with a specific tool?
If we know of several answers, the correctness of which will depend on hand tools or power tools, we should use the comments feature to establish the framework of the question, then answer the question. In this particular discussion, "which tools are available", we should encourage the use of "hand tools" and "power tools" tags.
I am somewhat new to Stack Exchange and have spent a lot of time as a newcomer perusing Stack Overflow. There, the OP poses a question, others ask for clarification in the comments and finally answers are generated. There is a wide use of tags, one of which is always operating system (mac?), developing environment(delphi) or language (Lisp). A question without this level of tagging would immediately be commented with a request for this minimal context.
No one would come up with a solution using Lisp until they knew the questioner was asking about a problem with Lisp.
Obviously, Woodworking is going in a less formal direction and we do not require that the user exhibit a level of resourcefulness on Google that has led them to hit brick wall and finally ask for help on the Stack. If we did required a wider search before asking questions here, I suspect few questions would make it to this particular Q&A forum. Oops, this is leading me in a new direction, somewhat off topic - I'll wait for an appropriate question, or perhaps ask my own meta question at another time.