I don't like the idea of it grabbing and cutting, and refilling and ...KISS
Aluminum with rubber-finger molded grip!! I think the crosswise grip versus handsaw grip.
The basic idea of a rope that would easily replace, like a chainsaw starter rope (knot jams against hole), with a pistol grip style of release, if possible, would be great. One side of the rope would be fixed/ attached, leaving a (15-20", without doing the math on a 5" branch??) length to be grabbed by the clamp (like the vice-grip grabbing mid-line). Maybe the rope should have overhand knots every 2" that would help to lock the cord behind the clamp.