
I know it's too late now, but in my kit I have super glue and cotton buds. If I do accidentally quick them, I put a drop of the superglue on the cotton bud and hold it to their toenail. Stops the bleeding immediately (even better than the styptic sticks) and seals it up. It's the same stuff as 'liquid skin' that's used for sealing wounds, so it's safe and hygenic.
The reason you put it on a cotton bud first though is to avoid gluing toes together (OOPS).