It'll be hard pushed.
Obviously you can try HGs. Although they are likely to be asleep when you land, you may find a papa who's keen to wake one if his stable for your business. Start phoning them as you clear Immigration - you've got nothing to lose.
Hardcore bros report the brothels in MK are likely to be still working. But that's a challenge for you to navigate unless you know a bit about where you're going, and the pickings may be slim. Worth a try if you're adventurous.
Anyway IMHO a better idea would be to hit up some of the 24hr girls - e.g. there are a couple I know in SWH. Must be some in most districts - but you'd need to read some profiles and make a list.
Alternatively, if you try the above and strike out, you can wait to the "11th hour" and still win ... If your flight is at 1:30pm, you do actually have time to hit a girl around Central or Sheung Wan at 11am - they are definitely starting work in SW by then. If you have a hair trigger you could even do two
and still make it to the Airport Express by 12:30 and make your flight with a brisk walk.
With that plan I'd definitely avoid TST - in Central / SW you can simply walk to the airport express - no risk of traffic jams.