Take your hand off the throttle if you're gliding, you're not using it any more. 'worst is it creeps open, and gives you a little power.
An argument could be made for a 100 series Cessna that between 0 and 10 flap, there could be a little benefit for stretching a glide, because you do create a little more lift, and can glide a bit more slowly. BUT, gliding more slowly will require a lot more skill and judgement to flare, with much less margin for error. You want the flap to slow you for landing, once you are assured of making the spot. Hopefully, you've judged well enough that you're comfortable committing to the landing a bit back, and can extend flap before the last minute.
Cessna specifies to glide the plane flaps up, so glide it that way. Cessna recommends the use of flaps for short field landings, so extend them as much as circumstances permit, as said, they can be in transit when you touch if needed. Bear in mind, and Cessna says, that if you really need to stop with heavy braking, the flaps should be retracted to put the most weight on the wheels. So, it could be that you're just getting the flaps extended as you touch down the main wheels, then retracting them right away, as you hold the nose light, and apply lots of braking.
Don't worry, when you have an actual emergency, it seems to go on forever, so you have lots of time!