To be honest, I am still scared to cut finish cuts with an axe. Something about it terrifies me. I have done it before, so I know it works and I know I can do it. But still, it makes me nervous. A good practice I have found is to rough out with an axe, and finish with a mallet-driven chisel or a large slick. For this purpose, I like to use my German Stichaxt.
An electric saw would be especially nice when working indoors. I don't like what 2-cycle fumes do to me!
It is interesting to see in tasks like this how different people and especially different traditions solved the same problems.