Electrum may connect to the Ledger without a firmware update, it's worth trying it first. If you have any trouble connecting, then you'll need to use Ledger Live to update the firmware.
Recently though, the pc where I installed electrum is quite unusable
You may be able to pull the hard drive from your old PC and extract the wallet file, if you feel it's worth the trouble. Of course you can use the Ledger to create a new Electrum wallet file, but any labels you applied to addresses or transactions will be lost, and any frozen coins or addresses will no longer be locked.