Shoelaces are a thing that is carried on one's person all the time, as part of the footwear. Such thing can be quite well enhanced to be dual-use.
A common modification is using parachute cord instead of the common lace. The advantage is the very high tensile strength, allowing other uses for the laces. The inside of the paracord also contains separate thinner strands, which can be extracted in times of need and used e.g. as a fishing line.
The design is fairly straightforward. A length of paracord is cut to match the length of the original shoelace. The sheath is pulled back about a centimeter, the center fibers are soaked with solvent-based glue, then the sheath is pulled over the glue-saturated part to make it one with the center and prevent its sliding back under mechanical abuse.
The ends are secured against fraying and mechanically strengthened to assist lacing by using a piece of a heat shrink tubing, adjusted to be partially over the sheath and partially over the inner fibers. The best kind was the 3-times shrinking, internally lined with hot-melt adhesive. A thorough warming with hot air (beware to not damage the fairly sensitive nylon sheath of the paracord) shrunk the tube and allowed the adhesive to penetrate the fibers and the sheath, forming a strong joint.
It turned out that the tube is just a tiny bit thicker over the sheath part to fit the holes of the given shoes. The outer diameter of the tube had to be reduced slightly.
The part of the tube over the sheath was heated with hot air and softened. Then it was carefully pulled through a die (a hole in a thick metal sheet, conveniently available in the mechanical parts bin) and cooled.
The resulting shoelace is solid, fraying-resistant, and heavy duty. The nylon sheath however has fairly low friction, which may compromise its ability to stay tied; more force is needed to secure the knots. Practical use will show more; during couple weeks of use the incidents of spontaneous untying were observed but were very infrequent.
A shoelace can be transformed to a garrote. A length of kevlar fiber can be folded inside the center part of the lace, secured to its ends. The sheath and optional inner fibers in the center part are weakened. When needed, the ends of the shoelace are wrapped around hands and pulled strongly, tearing it at its weakened center. The kevlar fiber is then pulled out and unfolded, forming a thin and very strong string with shoelace-wrapped ends acting as relatively comfortable handles.
A wire saw can be hidden in the same way. However, this one is metallic and therefore may be visible on xray or trip detectors. A possible variant can be a composite fiber, a strong polymer with a suitable abrasive (corundum, zirconia, silicon carbide? avoid tungsten carbide as that one has strong xray absorption, cubic boron nitride may be the best bet here) embedded to its surface.
Paracord, internal structure
Paracord, sheath pulled back, glue added
Paracord, sheath pulled back over glue
Heat-shrink tube, shrunk
Reducing the diameter with a die
Ends of the laces
Shoelaces in use