Again, welcome, bigdad. You and your wife have read too much Edgar Allen Poe!
There are very few cemeteries I have ever been to that has stands of oak and or cypress with hanging Spanish moss. The theory that Spanish moss is somehow ONLY found or generally found on weak, diseased trees is in error. It grows on perfectly healthy trees. I think what was meant was that when someone sees a disease/dying tree, and that there is Spanish moss on that tree, that person might blame the moss for the declining tree.
IF you simply don't like the moss, hey, there's nothing wrong with that. Get rid of it manually (if you can reach it all) or contact your local Extension Service and they will be able to put you in contact with someone that can rid you of the moss.