I usually take SQ17 YVR-ICN then connect to SQ15 ICN-SIN. It's 1 hour later arriving in SIN, but I have more time to have the break at SKL ICN. If you are in the same flight SQ17 all the way to SIN, I believe you have enough short time visit to SKL. Shower might not be possible. It's only an hour connection.
AFAIK, SQ17 in Y is pretty packed nowdays. So if you are all the way in the back of the plane, might take longer to get off the plane, and also longer line for security check.