Can I specify interfaces when I declare a member?
After thinking about this question for a while, it occurred to me that a static-duck-typed language might actually
TypeScript!
Well, ok... So it's a javascript superset and maybe does not constitute a "language", but this kind of static duck-typing is vital in TypeScript.

I don't see the point. Why not be explicit that the class implements the interface and have done with it? Implementing the interface is what tells other programmers that this class is supposed to behave in the way that interface defines. Simply having the same name and signature on a method conveys no guarantees that the intent of the designer was to perform similar actions with the method. That may be, but why leave it up for interpretation (and misuse)?
The reason you can "get away" with this successfully in dynamic languages has more to do with TDD than with the language itself. In my opinion, if the language offers the facility to give these sorts of guidance to others who use/view the code, you should use it. It actually improves clarity and is worth the few extra characters. In the case where you don't have access to do this, then an Adapter serves the same purpose of explicitly declaring how the interface relates to the other class.
D (http://dlang.org) is a statically compiled language and provides duck-typing via wrap() and unwrap() (http://dlang.org/phobos-prerelease/std_typecons.html#.unwrap).