With so many replies I might have missed the answer to the following:

Is it possible to claim clams by signing a message with your privkey?

Giving the privkey to some website, or some other software (even if it might be legit) is not a valid option.
I'm aware that you can first empty the BTC address to a new one, but that's not an option in some cases (like, giving up my sig address).
If signed proof isn't possible/planned, then I'll just ignore my clams to be on the safe side.