Steve, checking thru is the best,if like Dustin says, you ensure the bags are waiting to be transferred to the Silk flight @ SIN. The other issue taking CP is that you have to spend the night in SIN due to the scheduling change. I'm now transitioning to CP and find it's better to take CX881/883, stop in HKG, shower @ airport then have lunch with friends/shopping etc via the Airport Express train (30 mins to Central super on time!) then flying on to SIN @ 3ish on CX635, which arrives at 7ish in the evening in SIN, then you can spend the night eating well in SIN and jump on any flight the next morning.
As an alternative to the transit hotel, the Crowne Plaza in the airport itself is a great place. Rooms are great and if you take SQ, it's right @ T3 in SIN so you literally can hop into your room when you get off the plane. Another one is about 10-15 mins shuttle ride away, the Changi Village Hotel (formerly the Meridien) is a quaint change with a pool etc to unwind. Nothing fancy but beats staying in the airport. Decent food in Changi Village as well. There's no need to contend with traffic in hotels downtown.
One other alternative is the Grand Mercure Roxy, which is 15 mins taxi around the Katong area. Great area for local food and close enough to the airport yet avoid the rush hour nuttiness. I suggest you book a taxi with the hotel so you are assured transport to airport. Otherwise, great way to enjoy without getting too far away from the airport.
SQ37 is the best way to do it without any overnights etc.