I think this is probably fine, will give you a quick taste of the two cities and may help sway travel plans in the future, especially bearing in mind the 10 days includes travel time.

Leave NYC Day 1
Arrive SIN Day 3 around 1am local
Days 3, 4, and 5 Singapore
Evening flight to HKG
Days 6, 7, 8, 9 HKG
Day 10 fly to NYC, arriving same day

I'd say there's more varied things to do in Hong Kong and probably more travel time involved getting around (day trips to Lamma, Stanley, New Territories, Macau all possible), hence having more time in HK.