Should I send the rest in one go or divide into say 5-10 transactions? I know that will be more hassle and a bit more transaction cost but is it worth it in case of some unforeseen problem?
I'd send everything from the same address at once. For privacy, it doesn't hurt not to combine inputs from different addresses. In Bitcoin Core, enable "Settings > Options > Wallet > Enable coin control features". After this, on the Send tab, you can click Inputs.
If you have different addresses there, you can select one at a time to keep them separate (and send funds to a different address on your Ledger). Then click "Use available balance" to empty that entire
input.
I wouldn't send smaller chunks if you're planning to send everything. The risks (such as losing your seed phrase) are the same whether you send large or small amounts.
When selling (some of) your Bitcoin, it
does make sense to send and sell smaller amounts at once.
Just to be sure: when sending to a new address on your Ledger, you should verify that address on the Ledger's screen (and not just on your computer).
And should I leave 'Deduct fee from transaction amount' unchecked when sending from Bitcoin Core?
That tickbox is mainly useful when you're sending all funds at once.