The real trick in figuring out which length axe you need for mountaineering is to stand up straight and hold the axe by its head. If the spike falls below your ankle, then the axe is too long for you. Ideally, the spike should be somewhere between the bottom half of your calf and the top of your ankle.
I'm 6'. On a glacier climb, i.e. Mt. Rainier, I use a 60cm. My best advice is to try a 50cm first. If to short, move up in length by only 5cm.