A shutter-beam is the obvious trigger, you can trigger by breaking a beam of light or by sound, and they sell delay boxes as well.
What is the delay between firing your camera and the start of the exposure?
If you use a DSLR, can you shorten it by locking up the mirror?
Might you have to use two shutter-beams, one to trigger the shutter, and one to trigger the flash?
How short an exposure do you need to eliminate ambient?
Can you shorten the exposure by using the flash in manual mode (or by using a simple manual flash).
What is the duration of the flash?
Can you shorten this by using a big flash at low power?
I have a couple of shutter-beams, and there are numerous projects I am thinking about using them for... some of these will require a full range of movements... and a set of Schneider Apo-Digitars with Schneider Electronic Shutters.
They can be useful for simple pictures like consistently capturing a class of vaulters in the middle of the frame without having to allow a great deal of space for cropping,... for a high-jumper or a pirouetting ballet dance, the movements would be useful.
You could put the balloon on a bench, and prick it from underneath, or you could fill it with flammable gas (or liquid) and use a flame (from a suitable distance)