Although Kinabalu is fairly high, it's not at all difficult to climb and it can be done is a few hours by anyone who is fit.
There are plenty of very out of shape tourists that are poorly equipped on the trail every day and they also make it up to the summit.
No need for a tour, everyone is supposed to hire a guide and you can book a refuge by yourself easily.
The usual is to go up to the refuge the first day which can take from about an hour to 8 hours if you're extremely slow. Then they make you get up in the middle of the night to catch the sunrise which in my opinion is a complete waste of time. You get to line up behind throngs of people, it's very difficult to pass because of the lack of light, heavy traffic and uneven terrain, then you get to the top and maybe if you're lucky you'll be shivering along with a hundred people and see the sunrise if it's clear which is probably a 50/50 chance at best.
If you're fit, i think it's much better to start in the morning and go straight to the top, there will be no one there and you save the hassle of a night in the hut. Otherwise, sleep in and casually go up around nine or ten by which the crowds will be on their way down...