If they have interline, then they should. If they do, then you are correct - just transit. I'd call SQ to confirm.
If not, then you will have to go out and collect your bags. KE web check in probably won't work since you are going to China and they will have to check your visa status in person.
In that case, you'll have to use normal check in (or priority, if you have status). In the morning, the airport has been verrrrrry busy lately. If the KE check in lines are ridiculous, I'd go to web check in line as it is always shortest. When I flew to America last, the lines for normal check in snaked a ridiculous length, and I still waited 30-45 minutes in web check in line (which I didn't actually have...it didn't work for me).
Also, if you are in a crunch and security lines are long, show your BP to one of the staff in a blue jacket managing the line. At your scheduled boarding time, they will let you use crew security and immigration lines with no wait to rush you through.