A few cycles each in the fridge and freezer might help, if you're careful, and lucky. You should probably still have a back-up plan, if it doesn't work. and be prepared to keep the cheesecake for yourself if it doesn't end up quite right.
You will want to avoid freezing the cheesecake - as Ammnar Naseer said, that can affect the texture negatively because of the ice crystals that form. But what the freezer can do, especially in the very beginning, is cool the cheesecake more quickly. A few short sessions in the freezer will get it drop the temperature down much more quickly - but you will want to aim at fridge temperature, not a frozen temperature. Letting it sit in the fridge between sessions in the freezer will give it time to equalize the temperatures, so the middle will cool before the outside freezes.
I would not go longer than 10 or 15 min at a time in the freezer, and at least the same in the fridge between, generally. Maybe it can stand a little longer the first few times, when the temperature is still obviously above chilled, but shorten the cycles the closer your cheesecake is to reaching a refrigerated temperature. So using the freezer will buy you a bit of time, since the first part of chilling - getting the cheesecake down to fridge temperature - will go much more quickly for periodic exposure to a much cooler environment.
What it will not do, and might interfere with, is speed up what the rest of the chilling was supposed to do. This means whatever benefits come from resting at a refrigerated temperature, while the cheesecake slowly comes together, or the flavors meld, or the moisture equalizes, or whatever chemical thing that means a 12-hour resting is better than a (say) 4-hour one. Whatever that reaction is, it will probably happen slower at colder temperatures. It might happen faster at some temperature higher than the fridge, but probably the longer time is a good tradeoff for a safer resting temperature.
I'm drawing from this question which notices the difference between a four-hour chilled dough, and an overnight one. One set of time (I'm using the four hours from that question, but it will vary) is how long it will take the cheesecake to cool down. The other set of time is how long it will take to finish reacting once it is cool.
So, assuming you can use the freezer in a couple short bursts in the beginning to bring the temperature down to cool without leaving it too long and being frozen, you might shave several hours off the time needed in the fridge, and spend whatever time you have left resting at temperature as much as you can afford. Maybe that means you're heading out with a cheesecake chilled equivalent to 8 hours instead of 4 1/2. That is still less than ideal, but it may be better than you could do otherwise... and if you still don't like the looks of it at that point, or if it got accidentally over-frozen at some point, you can leave it to finish chilling for the next day while you take your backup plan.