And then simply send from original wallet to the newly created Ledger wallet? Or is this unsafe for some reason?
No, that's perfectly fine.
Also, if I do decide to set up my Nano S with Electrum, will I then be able to view it (and do everything else) in Ledger Live? In other words, if I make some transactions in the Electrum Nano S wallet, will I see those transactions in Ledger Live (and vice versa)?
Setting up the nano s (i.e. generating a seed, backing up the mnemonic code) does work without any software wallet.
You will set up your nano s without ledger live or electrum.
Then, afterwards, you are free to choose whatever you want.
The software wallet is just an interface to communicate with your hardware wallet. In consequence, the transactions you are doing will appear on both software wallets. They are fetching the information from server which have access to the blockchain.
So, yes. You will see the transactions in ledger live and electrum.