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While a router would be an excellent choice of tools to cut the recess the latch fits into.
I haven't done a knob and latch in ages and the last time I did, I carved it out with a chisel. I am certain that cutting it with a router would have produced a much smoother cut.
I would use a bit and drill for the smaller hole the rest of the latch mechanism rests in. As for the larger hole that the knobs shaft passes through, I have used hole saws in the same drill.
wbh1963 is flowing with the grain in Arlington, Washington, USA
A day without curls is like a day without sunshine!