You can not send BTC direct to Ledger Nano S because hardware wallet is not support importing of private keys, so you need Electrum as an intermediary for that. Since you clean your PC and if you install Electrum just import private keys in Electrum, wait for wallet for sync and then send all balance minus fee to Ledger Nano S.
I think my solution 2 was misunderstood. This is if you use Electrum to view your balance rather than Ledger Live. One would have needed to create their wallet this way:
As you can see on the bottom right of the 2nd screenshot, you can see the Ledger icon, indicating that this wallet was set up with a ledger hardware wallet.
You then sweep coins by inserting the private key.
By doing this method, you can actually send straight to the Nano S without having to create an new wallet to import privkeys. But this is assuming you use Electrum with the Nano S not Ledger Live or the Chromium extension.