I think you might find that a saw, particularly a decent small folding saw, will cut the sort of stuff you'd need for a shelter much faster than a small axe or hatchet will. A folded up Sven or Gerber saw in your pack would be a much better choice than any of the wire saws I've seen.

With a lot less chance of injury too.

Welcome to the fold.

JohnE
_________________________
JohnE

"and all the lousy little poets
comin round
tryin' to sound like Charlie Manson"

The Future/Leonard Cohen