Can I simply move coins using core to my ledger by sending them to my ledger address using the core client?
Yes.
Do I need to sync the client before it will allow me to send the coins?
If you have not received any coins after the time that your wallet is synced up to, then no.
If I send the coins will I lose my BCH?
No. BCH is an altcoin and anything that happens on BTC has no effect on BCH and vice versa.
If not how would I send my BCH?
You need to get a BCH client that can read your wallet file or you can import your private keys into. You can use the Bitcoin Core analogous software for BCH which is Bitcoin ABC.
Am I at any risk of a replay attack if I send my BTC and leave the BCH on the core wallet address?
No.
Any other considerations to be aware of when sending coins on an outdated version of core? I don't plan on using core once I've moved coins to my ledger.
Node policy has changed since 0.8 which makes some transactions that 0.8 may produce (just due to randomness) to be non-standard and thus not likely to propagate well. Furthermore, fee estimation has changed to be much better, and priority has been removed which will also effect how your client sets a transaction fee so you may end up paying too low of a fee for your transaction to confirm quickly. I highly suggest that you upgrade to Bitcoin Core 0.15 and let it fully sync. You can use pruned mode so that it takes up only a few GB of space instead of 140+ GB.
