I have been using Mycelium, Coinomi and Electrum mobile wallets and they are working great with me so far so good since 2017. You can actually set transaction fees on the first two wallets I've mentioned above except for Electrum which you cannot.
This is inaccurate. Regardless if you are using the mobile version of Electrum and its desktop wallet; you still have the options to manually change the transaction fees (sats/vbyte) by manually typing it or just simply using the slider. Also, it would be much better to check [1] https://jochen-hoenicke.de/queue/#0,24h to determine the least amount of sats/vbyte when broadcasting the transaction.