If I understand correctly, to claim CLAMS I only need to provide a signed message from the respective BTC or DOGE address. Is that correct?
Nearly, but not quite. You need to provide a signature, but of a transaction, not a message. This is the same that Bitcoin uses - when you want to spend your Bitcoins your wallet makes a transaction and signs it using your Bitcoin private key.
Unless I'm misunderstanding the original question, we seem to have gone off the track a little. Wetsuit just wants to find out if BTC/DOGE addresses are eligible to claim, right? Why would there be a need to sign a transaction by sending funds? Import the private keys and rescan the blockchain.
I'm just getting nervous about what will happen if a good portion of those "hundred thousand addresses" are eligible to claim.