Do whatever you have to do and go! You'll love it, and I bet you'll catch the fever and be planning to return again soon. Reminds me of one of my favorite quotes: "make the trip of a lifetime happen every year."
Also, I have shot elk with both trad bows and wheels. I think you are at no disadvantage with the stick, and in fact, I've had multiple encounters with bulls when I had the compound that I would have been better off with my longbow. Most of it comes down to being able to draw and let down slowly and smoothly, with less chance of spooking them. Not to mention carrying 3 fewer pounds in your hand all day every day.
And finally, I don't want to make this into a debate on it, but please shoot sturdy 2-bladed, single bevel broadheads. Trust me, I've learned from experience.