I use a tether attached to the head of my 70 cm ax. Its length is calibrated to stabilize my hand about 6-8 cm above the spike for either chopping steps or above the head placements when facing in on steep slopes. This length is also suitable for allowing me to switch hands when reversing direction on ascents of lower angles slopes without bothering to switch the tether back and forth between uphill hands at every switchback. Some people, as one poster mentioned, attach the tether to their harness. I never liked that when I was climbing because it was one more piece of rope near my Pearabiner(locking biner) when getting ready to belay, and I'm a BIG fan of the KISS principle when it comes to rope management and climbing in general. Also, attaching the tether to your harness would make it impossible to place the ax ubove the head without having a very long tether which could be very dangerous, IMO. Never tried it when not climbing simply because I don't wear a harness unless I'm roping up. The idea of attaching it to a cross body sling is interesting but, again, for me that would apply to a technical climbing situation. Otherwise, a sling is just one more piece of gear that add weight to your kit. The OP did not indicate he was going to be climbing so I think he could get by just fine with only a tether. My 2 cents.