Not that I've done any calling yet, I've read a lot about it and plan on trying it myself, have an E-caller, just not the opportunity yet.....Of the 2 you mention, the .204 would be the best choice for me, the 22mag doesn't do much for me and would limit your range. The .204 is real fur friendly if you're planning on selling hides, usually you'll get a small entrance and no exit, depending on bullet choice. Silverfox at PredatorMasters uses the .204 for yotes and is quite happy with it. .204 Handis and Ultras are gonna be extractors, so it may not be as fast as you'd like, so keep that in mind. You may still be able to order an ejector barrel, though, supposedly if you ask when you order.
Good luck, sounds like a lot of fun!!