Not really, that's how we usually do it too. Put water in, let it drizzle through the touch hole until it comes out clean, then pour a bit more, shake it, twist it over and let the water go out the muzzle.
It does not really matter when you clean your barrel from it either, if you have boiling water it should get rid of the remains. I usually clean it the next morning, it works just fine, I never had a musket misfire because there was shit left in the barrel.
The biggest problem is, that you can not pour it alone. You need at least 2 guys. We have no tea/coffee boiler, only a large kettle we can boil water in. The kettle does not have a handle or a nice funnel where the water comes out. It makes it difficult to pour water into the barrel without burning yourself.