You also might want to decide whether "airdropped" coin is worth to collect based on it's price and how much coin you have. You can use either
https://findmycoins.ninja/ or blockexplorer which support many altcoin to do that.
Once I sweep the key into Electrum, can I then sweep the same private key into another client that supports BCH and etc?
Yes and no: yes you can do this, but no it might not work as you expected. Not all Forkcoins have replay protection, which means they can move on multiple chains when you send one of them. Getting some Forkcoin dust and including it in your transaction prevents that.
It's been few years after many BTC fork created though. Fork which still alive and can be traded on exchange should already have replay protection.
For Bitcoin SV there is
electrumsv.io, but I have never used it and since BSV is a scam, I would not install that in my main computer. Better load it in a virtual machine. (if we are talking about lots of money, otherwise BSV is worthless so do not get into the trouble)
With crazy requirement to run BSV full node, i wonder how many Electrum server (for BSV coin) still running today. Even blockchair.com (block explorer) which support many altcoin, 2nd layer and token give up on BSV.