would it be better for me to just transfer all coins to my account on an exchange or a desktop wallet, and that way all funds are off my phone?
Yes, that's fine, but do not send it to any exchange except if you're planning to buy another digital currency.
The current recommended transaction fee (
based on Electrum's recommendation via mempool) is 10sat/b.
Sending them to another wallet/address isn't going to be expensive unless you have 100+ inputs.