Given the scenario you've outlined, it seems to me that a saw would be a highly practical addition. There is no more efficient tool for gathering wood or making shelter. And the weight penalty is minimal.
WARNING & DISCLAIMER:
SELECT AND USE OUTDOORS AND SURVIVAL EQUIPMENT, SUPPLIES AND TECHNIQUES AT YOUR OWN RISK. Information posted
on this forum is not reviewed for accuracy and may not be reliable, use at your own risk. Please
review the full WARNING & DISCLAIMER about information on this
site.