When I have to help a chick they usually don't dry fluffy. That gunk inside seems to be like a glue to their down. I've gently rinsed a chick in a cup of warm (95 to 100 Fahrenheit) water but it did not get all of it off, just enough that their wings and legs can work. In about a week it had all worn off.
You do not want to chill that chick so keep it in a warm place until it dries off.
About half the time I help one it dies anyway, there is often a reason it had trouble hatching. Some just aren't meant to make it. If you did not see any bleeding you are probably OK. That chick looks good to me.
You mentioned them hatching a little late. That can happen but are you sure you are counting the days correctly? An egg doesn't have a day's worth of development when you put it in the incubator. You say "one" 24 hours after you put it in. That's a common mistake. An easy way to check your counting is that the day or the week you put them in is the day of the week the 21 days is up. If they went in the incubator on a Thursday the 21 days is up on a Thursday.
If your hatch really is that late you might want to check your incubating temperature. it the average incubating temperature is a bit high the eggs can hatch early. If it is low they can be late. Two days early or late isn't horrible, that can and does happen even if the temperature is correct, but it is a red flag that you might want to check before your next hatch. I do not trust factory presets for temperature. Those can be off on the best of incubators.
