The deciding factor is, do you need your car seat in S'pore or not? If you need it, you definitely want to bring it on board. Don't ever check a car seat as luggage (too many get broken and lost).

If you are bringing the seat, just use it for take-off and landing if your child does better sleeping flat. You could just put the car seat to the side or under the seat when reclined.

Since S'pore is so easy to visit without a car (or perhaps you have friends/family providing one for your visit), you might want to look into renting or buying a CARES harness since the adult seat belt doesn't fit toddlers too well. It also might keep him "contained" better when he's supposed to be seated because it would be more like the car seat harness he's used to in the car.

Bulkhead seats are often recommended for families with little kids but that's less a factor in Business Class where the seats are further apart and the toddler wont disturb those in front anyway. I was going to recommend staying out of the upper deck and asking to be as far back as possible on the main deck. The advantage are access to the lavs and you can take him for walks more easily through Economy when there's no service going on. I found myself walking a lot with mine at that age. They tend to run on two speeds at that age; asleep or moving. My friends and I call it doing the "aisle laps". Much easier on a 747 when you can walk through Business too.

Don't fixate too much on getting him to sleep. It's so long that he will do that at some point. No one minds a happy, playing, quiet (ish) child. No need to make him suck on take-off and landing (common myth) so if he falls asleep on take-off, as they so often do, please leave him in Dreamland and don't wake him unnecessarily. That will make one less crying baby on board!