I don't use a mug but drink hot beverages out of my cooking pot, which is used only to boil water for rehydrating food in a zippered freezer bag. See the trailcooking.com site for ideas. I make tea (or rarely, coffee) with the leftover hot water. No dishes to wash!

I also do not attempt to carry my fuel canister in my pot. I use my stove only for dinner or (occasionally) for breakfast when my pack is unloaded anyway. The stove needs protection, but not the canister. To carry the canister, especially an 8 oz. one, in the pot requires a larger pot than I want to take (my solo pot is 0.55 L). Although for a short trip, my 2-person (1.3 L) pot will accommodate a 3.5 oz. Jetboil canister.

Your Mileage May Vary, of course!