There is no meaningful correlation between KYC and the safety of your coins. There are several big name service providers which have very strict KYC requirements which have been hacked, both for the KYC documents themselves as well as for the coins they are holding. Don't be fooled in to thinking that undergoing KYC offers you any sort of protection whatsoever - KYC only offers the exchange legal protection (or extra income when they sell your details to third parties).
Undergoing KYC to use an exchange is forgivable (although I would always recommend to use P2P or DEX trading and keep your documents safe), but you should
never be undergoing KYC just to use a wallet. It's bad enough that you are trusting an unknown third party to have complete control of your coins on your behalf. Why on Earth would you also be giving these internet strangers your personal details? Would you give your passport and credit card to a random stranger on the street for safekeeping?
The best site for estimating fees remains this one:
https://jochen-hoenicke.de/queue/#1,8h. Scroll down to the third graph "Mempool Size in MB" to get an idea of the size of all pending transactions at each fee level, and slot yourself in accordingly depending on your urgency.
I don't relate KYC with security but I said that web wallets that don't require KYC are not trusted as they get easily hacked while wallets like Xapo are apps that provide more security in terms of 2FA, ID verification in case you lose access to your wallet and plus ask an additional verification when you perform any transaction compared to web wallets.
Web wallets like coinbase are pretty reliable and in terms of getting hacked, they have an insurance to protect users but since they don't provide private keys, I don't prefer them.