RE: What gun would you use?
This really should be a 204 or a 22/250 or a 223 or a 243 thread.
The 22 or the 12 ga will work up to 50yds or so, and you have some overlapping in your deer calbers. Is it possible to swap one for a bolt rifle in a varmint caliber? 17hmr is a maybe out to 100 yds, ZERO pelt damage.
The 270 will do it, and the 30/06 will do it. Neither are best.