If there's one airport in this world where you don't have to worry about theft, it would be Singapore. Stay at the transit hotel and pick up your bags in the morning, they'll be perfectly safe.

That said, it would still be better all around (if a bit more expensive) to head straight to the city and your 'main' hotel in Singapore, even if you do need to pay an extra night. Then you can pick up your bags at the airport, get some sleep, and leave them in your room for the meeting.