"...do I just let the hot portion dangle off to the side? Normally I’d “cap” a wire if it wasn’t connected to anything but I don’t know if that concept exists with guitar wiring."

There shouldn't any wires that aren't connected. All your ground wires (black or bare wires from pickups) should be soldered to the back of the pots/switch lug/output jack per diagram.
All the "hot" wires (red or white from pickups) should be connected to pot lugs/switch lugs/output jack as per diagram. Again, forget about the colours in the diagram, just think "hot & ground" and the connection points of each.
Nothing unconnected or dangling