My horse has problems with this also and my vet will not give sedatives to owners. I'm sort of glad because if there's a problem, I want him to be around. Does your horse get sedated when his teeth are floated???? That's when I can really, really, clean my horse's sheath. In between times, he sees the vet for this and the vet sedates him. (For us, it's essential because he has other problems with his sheath.) You need a different vet. If you have a trailer, I'd haul him the hour to the other vet. Meanwhile, if he's a new horse to you, he might need his teeth checked? Just an idea.
It's not surprising that he's reluctant to drop if he was hurt when you attempted this the first time, but at least you know not to do that again. If he is really crusty and grungy, you might need to shoot some sheath cleaner up there and let it sit for a few minutes to lubricate it before you try to clean again. Use warm water. Be very careful. As he gets to know you, he might relax more.
Honestly, if it's a huge problem and he's new to you, I would haul him to the vet so he could be sedated. It needs to be cleaned. Otherwise, if you can wait till his teeth are floated, there's a great opportunity for you to clean his sheath. You can look at this as a plus: Your horse has standards! He's not going to let just anyone mess around with his equipment! <grin>