You should move your ETC to a wallet that you have the private keys (e.g. Myetherwallet). Not sure if there were any exchanges announcing support of the airdrop.
mew is not a wallet, it simple reads your private keys. you can use any other wallet that lets you export your private keys, then upload to mew.
You can send your ETC to the concerned classicetherwallet, there also we have to private where it can trace to get the Callisto airdrop. Only two days left for snapshot so this is the right time to send ETC tokens.