Lots of similar threads here you might want to take a look at.

Singapore is easy to explore on your own. I'd skip the organized tour. Pick something you'd like to see that opens early enough and just hop on the MRT. Ideally you would select something near to the MRT line so you don't spend a lot of time getting there.

You will get sweaty though as Singapore is very tropical. So if you have lounge access or another way to take a quick shower when you get back to the airport that would be a good thing. How long is your onward flight?

Another option would be to just pick a hotel and stay in town. Get up early and see a thing or two. Then grab a quick shower before you head back to the airport.