Yes, I'm sure the Shangri-la will offer you the opportunity to change & shower in the spa or pool area.

At Changi Terminal 1 (i.e. not SQ), I have used a spa area for a shower/change on arrival before going to the office. It may also be worth checking out the in-airport hotel which may offer this service......certainly seems to make better sense than booking a F class SIN-KUL fare!