buying a SIN-KUL flight upon arrival at Changi, with no checked bags
I'm flying from the East Coast to SIN via SFO on United next week. I'm hoping to add almost a day on the front end via same-day change so that I can make a one-night trip to KUL upon arrival to SIN. (This is my first time to Asia; I didn't expect to have an extra day on the front end, and I didn't know that SIN-KUL flights are so cheap.) I won't know if I can make the outbound flight change until about a day before, so I want to leave my existing SIN (and SFO) reservations/plans unchanged. The SIN-KUL would have to be upon arrival or not at all.
Rather than book a SIN-KUL flight in advance and then risk missing it (or arriving hours too early), I was hoping to buy a ticket upon arrival to Changi. Has anyone here done this before? If so, do the SIN-KUL flights generally have walk-up availability throughout the day (this would be a Tuesday morning), or do the flights tend to sell out? Do the fares stay in the $50 r/t range or do fares spike for same-day bookings? I'd probably have to choose based on schedule rather than carrier, but is there a big reliability/service difference between Jetstar, AirAsia, or Scoot?
Thanks very much for all feedback.