I usually buy 2 tickets, one to SIN and then SQ or a LCC to SGN. If SQ, bags can be interlined. Changi is very easy either way.

This could be cheaper too. No frills Y for a short segment isn’t a big deal for me but others MMV

So for the OP look at ORD-SIN//HKG-ORD or ORD-HKG RT and a separate ticket to/from SGN