Seems you have not been in Singapore yet, otherwise you would not be such optimist.

From Changi to the bus stop at Woodlands Checkpoint it is 90 minutes minimum using MRT - You need to change twice at Tanah Merah and City Hall. Then you need to wait for bus at Marsiling. Bus can come in 2 min or in 20.min. Now, there are just three bus stops from MRT to the train checkpoint but if the road is jammed you might spend more time standing in that bus than walking that three stops. That's from personal example.

Then - while immigration to/from Singapore won't take much time, you have no guarantees what Malaysian customs situation looks like. My personal example - two hours and 15 min wait on that side on arrival. Granted, it was on three days weekend but still - you need to expect that it won't be breeze.

Finally - did you already bought the train ticket? Because you should not count that you can walk in and get that ticket - you are not alone. You can go to JB Sentral to Woodlands KTM & ETS Train Ticket Online Booking | KTMTrain.com and key in your date and see if train tickets on either or both directions are available.