My question is if one shares bitcoin address and signature is there any risk of a attacker to compute the private key with this knowledge
While signing, the public key becomes exposed. The primary assumption is "It's impossible to find the private key which relates to a known public key", and this assumption isn't likely to be disproved (in other words, cracked) in the next 10 years.
The process of signing a message to claim airdrops is absolutely safe, as you can move your coins to a different address after claiming your airdrops.
The only risk is your privacy: They'll know how much money you have. If that's an issue, you can just mix your coins after you're done.