It depends on whether the purpose of your visit is personal or business
But i guess you are talking about general leisure clothing. Singapore is a quite formal city with a lot or airconditioned space, especially shopping areas. I would opt for long trousers in a cool fabric (ie not jeans) and a short-sleeved shirt.
If you're going to Singapore, take a jacket or jumper: I have rarely been colder inside than I have been in Singapore: they really pump up the air-conditioning in some places.
To answer the question as put: I don't recall seeing men in Singapore or Hong Kong wearing shorts. I don't think it would cause any particular problems, but you'd stand out. Some better restaurants might look at them a bit askance, too.
I haven't been to Vietnam, so I can't comment about there.