I built this shed in the backyard, it has a dedicated 20amp GFCI
circuit running to it. Once inside the shed (it comes in from the
floor) I have it hit a junction box and branch out to the various
spots i need it (outlets/lights etc.).

My question is, do I HAVE to run the wire through the studs (drilling
a lot of holes because studs are 16 on center)? or can I run it on the
surface of the wood, near the top sill? what are my options? I have a
work bench, am I allowed to run it under the work surface, and staple
it to the underside? any thoughts as to how I can avoid drilling a
bunch of holes?

I live in norfolk, va...