You can try cleaning it, certainly. I'm afraid that you may not get stellar results or lengthy coil life, but if you can't get another coil for 4 days, you can't. You can soak it overnight in something like everclear than rinse thoroughly and dry. I don't know how your coils will fare, every coil is a bit different.
I used to clean my Nautilus 2 coils in a similar fashion but stopped the practice, due to the fact that coil life was unpredictable and I wasn't really sure how clean they were getting.
In your situation it would probably be preferable to vaping a burnt coil, really not advised. Once you've clean the coil, you should treat it like new and reprime it.
Also, IDK your location, but if you like the tank and it's working for you, when you can you might want to order a few boxes of coils, and your cheapest way to do that would most likely be a Chinese vendor, as far as price. You'd need enough coils to keep you going until you get in that "cycle."
If I have a drop in coil tank I like I tend to make sure that I have several boxes of backup coils, when/as I can afford to do so, etc.
Good luck,
Anna