Skrill and Paxful are legit companies and your info would be probably safe. There are really no alternative to payment processor like Skrill so there's no other options than providing them with your KYC so is paxful for some countries. But I'm not sure about the exchanger you mentioned. Exchanger asks KYC when you are exchanging large amount in or from fiat and not necessarily with a mal-intention but I'd still try my best not to provide my KYC as much as possible.