If you are looking for an exchange free from KYC and support with BTC segwit deposit seems difficult because all exchange are required with KYC and better use personal wallet like Trustwallet if you want get segwit btc address without need KYC.
Not all exchanges require KYC and you can deposit Bitcoins into decentralized exchanges that support SegWit transactions. Having said that, trust wallet is not a good wallet to use for Bitcoin, they generate only one receiving address for you and that's terrible for privacy, recommended wallets like electrum generates only native segwit addresses and you can generate as many addresses as possible, so why use a closed source wallet like trust wallet that isn't good for privacy.