That's not how it works.
To claim your CLAMs you need to sign a transaction using your BTC private keys. There's no mechanism to claim your CLAMs simply by signing a message.
Your CLAM private keys are *the same* as your BTC private keys. You claim your CLAMs in exactly the same way as you spend your BTC - by signing a transaction using your BTC private key.
Signed messages aren't going to help you.
What you could do:
1. download the CLAM client on your online machine
2. run it, and let it sync up to at least block 10,000
3. shut it down, and copy the client and the whole CLAM data directory onto your offline machine
4. on the offline machine, import your BTC private keys; let it rescan the first 10k blocks
5. on the offline machine, create a transaction that spends your CLAMs; maybe to your exchange deposit address
6. on the offline machine, 'getrawtransaction
7. copy the raw transaction information to the online machine
8. on the online machine, 'sendrawtransaction
That way you've not exposed your private keys to anything other than the offline machine.
I made as you describe but when I insert in the console my BTC address private key it says that it's not a valid private key (error -5).
I write importprivkey