Would it be too extreme to simply walk on your horse for two/three weeks once cleared for riding (you said about your fourth week)? If this was me, perhaps because I'm naturally not one to push my luck, and have experienced riding after surgery, I would simply walk my horse until the actual healing period is up. Walking is something that is so overlooked with riding in general, but is such a useful tool! It will allow you to still feel like you're doing something with your horse, and also improve on whatever exercises you like to do at the walk.
I'd be hesitant to do a lot of trotting, as the action of the trot may make your surgery area feel more tender/cause issues, especially if it affects your core... but like I said above, I'm one to be a little too cautious after surgery, haha!
All the best!!
♥ Seoul Searchin' for the Lovebug ♥