A 22 Hornet would be legal by definition, as would the 17. The only �caliber� restriction is placed on the use of rimfire cartridges for big game.
As I recall, a couple of Coasties used a 223 with Sierra varmint bullets to take a good-sized bear on Kodiak a few years ago......FWIW. But Phil�s advice is where I�d start, and there may be some hunting conditions where more would be prudent.
Sometimes, the air you 'let in'matters less than the air you 'let out'.
