I was going to suggest 3M Super 77, but I'm not so sure it will dry completely colorless. One of the only adhesives I can think of that will dry absolutely crystal clear is that stuff used to fix windshield chips. It cures under UV light.
Downtube placement would likely be the easiest to conceal the cable for a clean installation. Running the cable from the mid-tube position might prove difficult. This build is turning out to be sweeter than saccharine!
If you're not going to refinish the paint, then the crusty beehive is the way to go. I will say that I prefer the brushed aluminum rims over the black enamel one, so hopefully you'll get the fitment worked out.
TRM beat me to it, but yeah, it's far easier to source a replacement axle! I use hex jamb-nuts to hold the axle secure in a bench vise while I do the filing--one side then the other. Helps keep everything nice and parallel. Go slow and deliberate...you can always take off more.
Looks like the disc adapter simply spins onto the hub, like a freewheel would. Which would make that a rear wheel, reversed and mounted up front? Now, I'm curious, too.
For that style of intricate pattern, I'd suggest that frisket paper is superior to common masking tape. Find it in art supply stores. It's likely to eliminate any pesky bleed-through and deliver crisp edges.