So Electrum docs say to move your coins to a new wallet before splitting using the private keys of the old wallet. How do I do that? I've already created a new wallet. If I use a regular network transaction I have to pay fees. There has to be a way to do this from withing Electrum.
Don't sweep the coins. Just send a transaction using the max button and set the slider to be within 25 blocks if you don't need the coins quickly as it'll give you a good low fee to use instead.