I don't understand why we are forced to give out our private key of our wallet in order to claim bitcore. There are many other airdrops with no such requirement. And if we own a hardware wallet (ledger nano s), a safe way you say is to move your coins to new wallet and claim using old wallet.

Can I create a new wallet inside ledger nano s that has its own private key? If so how can I do this?

Other than that, with my current private key tied to other wallets like ethereum, etc, stratis and many others, this claim would be really troublesome for us hardware wallet owners.

I suggest you use message signing option to distribute coins instead of asking private keys.

Edit: (Added a missing word)