Just use a decentralized exchange, I'm always using
https://flake.exchange and it does exactly what you're describing. BTC to USDT or ETH, without KYC, connects straight from wallet, and swaps goes absolute instant
I had never heard of flake.exchange before. I just visited the site - it looks impressive.
Do you happen to know whether they use atomic swaps, or is there theoretically a possibility that I could send my bitcoins and not receive the requested tokens?
And one more question. You say the exchange happens instantly. Instantly - after how many network confirmations (if I am sending bitcoins)?
As for the OP, I would also suggest taking a look at b1exch.io. It does not fully meet the stated requirements, because there is a short period of time when you do not control your coins: one cryptocurrency has already been sent, while the other has not yet been received. However, unlike flack.exchange, which positions itself as an aggregator (that is, it only connects you with other platforms and does not participate in the swaps itself), b1exch.io handles all swaps on its own and risks its own reputation with every transaction.