Spreading silicone caulk thin?
Two ideas: A plastic putty knife, or a shower squeegee.

Plastic disposable putty knifes are sold in most paint sections and are cheap and somewhat flexible.  I've seen them up to 6" wide.

Another common item would be a rubber-edged squeegee commonly sold to dry off glass showers to prevent water spotting.  The flexible rubber might make it hard to control the thickness of the silicone, but it seems like it would be worth a try.