For skins, the wool starts to slip up here by December, so you can send them any time between shearing and then. Obviously you want the wool to have grown back long enough to make a nice rug. If you want to make a jacket or something like that, you would send it off fairly soon after shearing, or they can trim it for you at the tanners.
Our sheep don't need their bellies trimmed (fortunately), so I'm not sure how that would affect the skins as I don't know how wide from the midline you need to trim - check with the tanner and the abattoir or slaughterman.