Just throwing an idea out there: do the same as for pointers with unknown nullability.
func maybeThisCanThrow() throws!
This is an implicitly trapping throwing function: exceptions thrown from that function will trap unless the caller makes the call within a try expression:
try maybeThisCanThrow() // now you handle the exception
maybeThisCanThrow() // implicitly prefixed with `try!`
The compiler won't emit an error if you fail to use try, it'll just trap as if you had written try!. This is similar to implicitly unwrapped nil pointers.
Note that this behavior can be added later. I don't think there's a conflict with what is proposed here. Implicitly trapping throws! can be a future direction.