Climhazzard in Japanese is クライムハザード (Kuraimu Hazado). Phonetically, Kuraimu is either
Crime or
Climb, while Hazado is
Hazard.
Crime could work, for all the reasons listed above. I, however, am partial to
Climb. After running through an enemy with his sword, Cloud essentially "climbs" up into the air. This is consistent with at least one dictionary definition of the word "climb":
Full Definition of climb
intransitive verb
1 a : to go upward with gradual or continuous progress : rise, ascend <watching the smoke climb>
If you observe Climhazzard in other games, you'll see that while aspects of the swordplay vary, this Limit Break always incorporates a sharp, rapid ascent into the air from either the ground or the enemy itself. (In the case of Advent Children, Cloud quite-literally
climbs Bahamut SIN as he bifurcates him, before leaping even higher into the sky).