I've only seen a running braid on one horse in competition- a purebred Arabian. A person that I used to ride with had an Arabian mare that she evented and she looked horrid with a short mane. So, she just did a running braid after she grew it out.
I wouldn't recommend trying it with that short of a mane. I would chop a couple of inches off and do some buttons. Or not at all if you are doing jumpers as it doesn't really matter.
I'm with MIE- I like something to grab ahold of in those "holy s***" moments