if there's no other better alternatives and you're willing to consider an indoor venue, you might want to try Gymmeland -
http://www.gymmeland.com.hk/ on robinson road. the venue is probably available at short notice. however, other than drinks, snacks and utensils, you will have to source your own food and cake. i'm planning my son's 3rd birthday party there this week and it's also last minute. I attended a 3 year old party there a few weeks ago, it's not bad, at least the kids are entertained. given a choice, i would have gone for My Gym -
http://www.mygymhk.com/ but you usually need a few months advance notice there. however, it's not an outdoor thingy that you prefer but they do organise some activities for the kids and they also have a projector where you can show pictures and video of your child on the screen. besides some climbing and relay games, my favorite part is arts & craft where each child is given a white flower pot and colorful markers to design the pot and let them bring it home. the thing is the venue is quite small unlike My Gym, but 15 kids should be just about the right size. call them for more info. hope this helps.
one more thing, if you have friends who are member of the Aberdeen Marina Club, that would have been perfect. their adventure zone is suitable for both children and adults, simply superb!
good luck!
gwen