The idea itself is not a problem for your privacy if you do it right.
I would recommend an exchange from BTC to USDT for example on ChangeNow (as far as I know they have a few problems right now, but in itself it’s very trustworthy) or SideShift (has always worked well for me!).
When choosing the USDT wallet make sure to either use a hardware wallet, or if you don’t have one and don’t want to get one then at least not keep it on an exchange (Coinbase, Binance etc.) but use a trustworthy USDT wallet such as MyEtherWallet.
I haven’t tested KuCoin myself, so unfortunately I can’t say anything about it, but I’ve only heard good things about it!
In order to avoid unnecessary losses due to wrong address, keep in mind that there are different chain types (OMNI, ERC20, TRC20 etc.) when making USDT transfers.
If you want to know more about it just reply and I will show you.