there are transit hotels airside at SIN T1, T2, T3 and there is an airside transfer shuttle from T4 to T2, but you need to have a transfer service. If you have one ticket, the transfer would be included. If you have two separate tickets, there is a transfer desk that checks and you'll probably have to exit through immigration and take the landside bus...
But immigration is very quick, so shouldn't add a lot of time...
I will only have carry on luggage, and should be able to check in online for the next flight. So I don't think transfer service will be needed. Am I missing something here?