It has been a while since I have joined an airdrop. From my experience, none of them has asked me to sign anything. Airdrops are supposed to be free and you do not need to send anything to them. Anyone asking you to send first are scams.
Sometimes I thinks one might appreciate signs up before it get to ones wallet, what if is not safe and u got it without your consent and it becomes a problem. However, I prefer it in an exchange than in my private wallet. Exchange wallet could come as result of holding certain coin and exchanges will be responsible for security check-up of such coin.