You can use Coinomi or Mycelium I think you can swap USDT right on the app if I am not mistaken. For fees, I think they are also customizable. Just don't use untrusted wallets or else your funds will be gone. I've been using those apps I've mentioned since 2017 and it's working well though I have never tried swapping USDT but with other coins yeah it's good.
OP wants a Bitcoin wallet, not a multi-coin crypto wallet like Coinomi, this is a bad choice, also Coinomi is not an open-source crypto wallet, I have lost my digital asset using that wallet before and at first, I thought the fault was all mine until later I started seeing other people having the same problem.
Crypto wallets Like Coinomi are a bad choice choice, if you really care about safety it is best to choose a open source non-custodial Crypto wallet, many people in this thread have already said the best ones, this doesn't count.
TRZEOR, Electrum, Blue wallet, Unstoppable, and every open source Bitcoin wallets out there are excellent choice, some called themselves open-source to mislead people, verify from people who have used such wallets before.
I verified that Electrum, Unstoppable, Trezor, Safepal, and Keystone are very reliable choices to store your Bitcoin.