(In my limited experience) I've never found need for a small (read wire) saw. If a person has a knife or a machete, or a leatherman multi-tool, or if they have the physical capacity to snap small sticks, they can do without a saw. (for wood, anyway) If space is so limited, I'd rather have vitamins, .22 ammo, matches, fishhooks and line, neosporin, chlorine tablets, etc... However, a different wire could be useful for snaring. Given the option, pack a real saw!
Like Tony said, Welcome to the forums!
JMHO
