I also tried to withdraw less than $10 on bybit and binance and the exchanges would not allow me to withdraw...I think I saw a video a while back where they recommended withdrawing $1 first to test (to make sure I choose the right network etc). The other day I tried to withdraw 4 dollars with bybit and binance and I got the message: the withdrawal is less than the minimum allowed.
Bybit has minimal withdrawal amount - 0.001 BTC, so you can't withdraw 10$ via bitcoin network. Binance has very expensive withdrawal of many coins. If you are not afraid of KYC, it is better to use FTX exchange, there withdrawal of bitcoin and most altcoins is free.