I have historically been in same boat.
Never saw a bone except skull plate. Debone all other body parts in about 15 min.
I had never skinned the head off, but shot a buck worthy of a mount this year, but not so worthy I could resort to a Euro, so I tried it, following my taxi's advice around ears and lips, though could have done better at bases. Anyway, it wasn't hard, didn't take long, and after I removed the easy goodies off it, the skull was quite light and not likely worth carrying a saw for(yay!).
That said, elk are another story and skull capping those buggers can be a pain in the A$$. I've used a few smaller folder, but broke as many as I didn't. WY saws are great in a Horse Pannier, but not my daypack. Love more ideas specifically for skull capping Elk/Moose sized critters.
PS I'd love to shoot a Bighorn, but would hate to carry a mature rams skull out. Some day I'll suffer through that, or hopefully my 20 something son will carry it for old dad.