Stone nails won’t work. They break to easy. However. Wood nails work well. So long as the hole is drilled for the wooden nail to pass through. Using another log to hammer the nail through the hole in each piece of wood. Nails the 2 pieces of wood together.
Both parts require the hole for the wooden peg/nail to be drilled first. You can do this with a sufficiently sharp enough knife. Stone…heh, maybe for game purposes. But a stone blade would be slow to do this in order to avoid snapping the stone. It takes about an hour per connection including the wood nail, using a stone knife.
Metal blades without much worry of breaking the blade wouldn’t take as long.