The concept of base is closely related to ints, and the base argument is useful for a large percentage of the types that int accepts. It is not related to strings, in general, and applies to only one of the types it accepts. In one case "not a float, etc." applies to a very limited set of types, in the other case it applies to every conceivable type (except int).
That suggests that it would be better to simply add an int method: