I have a Raspberry Pi 4 with 8gb ram which could do this, using a fresh Ubuntu install. Can I copy the blockchain files (not wallet!) from my offline installation of Bitcoin core to save me some time? That way it would only have a few days worth of blockhain to update.
This should work, but why use a full Bitcoin Core installation just to broadcast your transaction? You can get a Tor browser (for privacy) and use
https://coinb.in/#broadcast (or many other websites) to broadcast the raw transaction.
Is there any point in doing an upgradewallet with my original wallet in the offline Bitcoin Core?
I can't answer this. If it's working, I wouldn't touch it, but it might be worth it if you currently don't have spare addresses in the keypool (which means you need to make new backups).
Finally, once Ledger set up, is there any risk/implications in transferring a test amount (like 1 to 10 mBTC) so I can get the hang of things?
Read this:
Five Ways to Lose Money with Bitcoin Change Addresses, especially the part under "1. Backup Failure".
Modern wallets prevent this, your old wallet may still have this risk.