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 would probably do multiple transactions, though you can't really hide your stash that way. But I would prefer to have not so large UTXOs aka coins in my wallet. If you make a large transaction in one go you end up with one big UTXO in your new wallet. Any spend from this will usually reveal your wealth by spending your large change coin/UTXO.
(If the terms don't ring a bell in your head: brush up your Bitcoin knowledge at
https://learnmeabitcoin.com)
And should I leave 'Deduct fee from transaction amount' unchecked when sending from Bitcoin Core?
As you are transfering from your original wallet to another one of your own, it doesn't much matter. Say you decide to transfer 1 BTC with 'Deduct fee from transaction amount' checked, i.e. your wallet balance is reduced by exactly 1 BTC by the transaction. The transfered amount to your destination wallet is less than 1 BTC as the fee is taken from the 1 BTC away.
If 'Deduct fee from transaction amount' is unchecked, your destination wallet will receive exactly 1 BTC and your source wallet balance is reduced by 1 BTC plus transaction fees.
To see what's currently necessary for transfer fees, you can have a look at
https://mempool.space as at the moment there's quite some transactions congestion and fees are rather high.
Be careful when you copy/paste transfer destination addresses. Always check if destination address is correct and unaltered (by clipboard malware or similar nasty things).