According to UA rules, a stopover is less then 24 hours, so one SWU will cover SIN-HKG-NRT-LAX. However, UA's computers - and especially agents - don't know this and assume you will be checking in seperately for SIN-HKG and then HKG-NRT-LAX.

Try and work with UA Customer Service to get one SWU to cover the whole shebang and, if successful, be absolutely sure you get all three (SIN-HKG, HKG-NRT, NRT-LAX) BPs when you check in at SIN. That way, that one SWU will cover all segments. If you do not, HKG will probably demand a SWU for HKG-NRT-LAX when you check in and if you don't surrender it, they may park you in Economy.

If SIN refuses to check you all the way through, expect to eat two SWUs and then fight with UA Customer Service after that fact to get the second SWU re-deposited.

Also, if you are on an H or higher fare, 30K miles will cover the whole shebang (even if you spent more then 24 hours in HKG). Might be worth it to save the hassle and worry. If you're on a lower fare, then this would not be an option.