Skinnies are going to be 265 to 285 - a 35x10.5 would be like a 265/90r16. I've never heard of one. I think you need to go 315/75r16 if you want a 35 inch tire on a 16 inch rim.
The only tall skinnies beyond 33's that I'm aware of are super swampers. They do have sizes for 16" wheels, but you'll have more selection with a 15" wheel. Check out Summit Racing, they list just about every size imaginable.