visas – Chinese citizen, transit through Hong Kong then Singapore to a third country

I’m a Chinese citizen (PRC) and I currently reside on the United Kingdom (LTR Residence). I’ll be going to China later this year and I’d like to visit Hong Kong and Singapore before I return to the United Kingdom.

Both Hong Kong and Singapore offer visa free entry if I’m using the country as a transit, (7 days for HK and 4 days for Singapore). However HK requires evidence that you hold the correct permits for the transit country, in this case I wouldn’t have any documents to prove this aside from a flight from Singapore to UK.

So I guess my question is: Is it possible for a Chinese citizen to travel through PRC -> HK -> Singapore -> Third Country without needing a visa for HK and Singapore? I cannot prove I have a permit for Singapore as I will also be using this as a transit to the UK (Which I can prove).

Otherwise I can always apply for an EEP for HK, however I’m unsure on how long this will take and whether or not I need to do this in person.