No, you don't want to give away the priv keys, as someone may transmit a future transaction you could claim with it. Simply signing a message would be sufficient. Don't reuse the 'k' value with your ecdsa sig!

Of course, you just have to prove that you know the private key. Handing it out is unnecessary. My bad.

BTW, instead of signing a message, you could also move around some money through that account. This may be easier to achieve for non-tech people, as it can be done with any Bitcoin client.