RE: shotgun scope size
Like some people has already said, you put a shotgun scope on a shotgun.
First off you have to look at the construction of the scope. A shotgun has a different type of recoil than a rifle and so the internals are built different for a shotgun scope - compared to a rifle scope.
Second off is the fact that a rifle scope is usually made to be shot at 100 yards and beyond. The parrellax is designed into the scope for it to be shot that way.
An average shot with a shotgun is 50 yards or less. So a shotgun scope is designed to be used that way. Not at 100 yards and beyond.
So looking at rifle scopes to put on any shotgun is a waste of time.
However,
A muzzleloader scope will work on a shotgun - I am told and will do a good job for what you intend to use it for. They don't make 50 mm muzzleloader scopes - as far as I know.
Go to a real gunshop that has a knowledgeable staff that can help you choose the right scope for the job. Make sure that the scope has a lifetime warranty - so if there is a problem, you can get it fixed and it won't have to come out of your pocket a second time.