Install Electron-Cash (note the slightly different name , electron, that distinguishes it from the original electrum).
The first release of Electron-Cash had an annoying bug whereby it looked for wallets in the same folder as Electrum: this may have been fixed by now (I haven't checked), but avoid making any transactions until you're sure. You do have the option of specifying a wallet folder of your own choosing.
Once you've ascertained that you're using separate wallet folders for Electron-Cash versus Electrum, you should copy (not move!) your old wallet file from your Electrum wallets folder into your Electron-Cash wallets folder. Make life easier for yourself by giving it a recognizable name (if the old wallet file is called default_wallet, then use some other name, perhaps BCHdefault_wallet, for your new copy).
In Electron-Cash, open your newly copied wallet (if you took the precaution of giving it a distinct name, then you'll have to specify that name in order to open it). You are now viewing your balance of BCH at an identical address/addresses to your BTC balance. BCH has built-in replay protection, so you can safely move them to some other address without accidentally moving your BTC. Obviously, the safest place to send this is an address (controlled by you) that doesn't have any BTC in it.
There's nothing to stop you from sending them to an unused address in the same wallet, but if you do that, you would then want to go to your BTC wallet (Electrum) and mark that address as "frozen" (and in the new BCH wallet you would want to "freeze" any addresses, including change addresses, that you know, from looking in your old wallet, to have BTC in them).
For any future forks, don't blindly assume that replay protection is built-in. It was for the August 2017 fork, but you'll have to do your own research next time!