The opening needs to be 4" round. I do not have a 4" hole saw and don't
really want to buy one as I'll probably never use it again.

By the time you get some kind of crude opening hacked through the timber you'll
really wish you'd used the hole saw.
Be smart, buy a 4 1/8" hole saw and arbor. You can use it for cutting speaker
holes in door cards, window openings in kiddy toys, etc. Milwaukee makes good
ones, most box store brands will work fine. Prices aren't all that steep
considering the time saved. Good luck.

Joe