I haven't done SAR, but I often walk the dog on trails that get over grown with blackberries, scotch broom, and blocked by occasional deadfall. I carry an large fanny pack with bags to handle the dog's business, and a few tools. The current set are:
- Mora 2000 sheath knife. In its green plastic sheath it could almost pass for a stick.
- Fiskars pruning knife (the blade retracts into the handle); for branches upto a couple of inches in diameter.
- Corona (from Lowes) folding garden clipper. The least threatening cutting tool I can think of.
This is my third pair of folding shears. These are like multitools, but have a garden clipper instead of pliers. At around $20-25 none have been high cost or quality, with the riveted pivot eventually breaking. But the convenience has been worth it. It also has a knife, saw and weeding tool, but I don't find these very useful.