What honestly do you mean about local trader this is mycelium section where only mycelium walle only are here maybe you are talking about bitcoin account from some traders .. i think there is no trading site are giving you private keys/secret keys they are just exchange site and they are not providing any private keys or ways to backup or export secret/private keys.
Better to explain to us what is local trader account you mean,, ?
Mycellium allows you to sell your bitcoins locally thru local trader system but electrum does not supports that.
OP you need to recover your account in mycellium,once you have done that, click on Buy/Sell, Open Market and swipe from right to left 5 times and you will see "My info" Tab,once you are on that Tab, click on 3 Dots on the header and backup your trader identity (Public key/Private key)
