How does this work?
No offense, but the short answer is "poorly"...
Green stuff isn't going to hold your part any better than your favorite flavor of cyanoacrylate adhesive... One good hit and you will end up with two pieces (one, after you misplace the broken piece somewhere) and a messed up paint job (assuming you keep track of the part long enough to try and repair it.
There is a good reason so many people pin stuff; it works.
I've had two miniatures take dives off of the same 5 foot height shelf and while glue and green stuff separate, the pins hold the part in place... Granted, I've needed to re-glue the joint, but if all I was using was an adhesive I'd probably still be looking for the parts.
So how do you pin an extremely thin piece?
You've got a good start with a pin vise and the old aerial wire...
Next, check the part you want to join. Is the wire at least a little thinner than the part? If not, this will never work... (Note: I can't remember if the old aerial wire is .015 (.38mm) or .020 (.51mm). If it is .020, than you can get some .015 and you might still be able to pin it. If it IS .015, I've never seen anything thinner... Also, when asking for it at a hobby shop, it is sometimes referred to as "Music Wire").
Assuming you have enough to work with, do you have a Dremel and a sanding wheel? If so, run it along the outer edge of the tip of the wire to file down any burrs from cutting. I like to go a step further and make the tip into a wedge. That way when you insert the wire into the hole and add a little pressure, it will bite in and keep the part from rotating (rotation over the axis of the wire will break your glue's bound faster than a blow).
Next, I would suggest prepping both parts. Clean up the edges you plan to join with a light sanding on the outer edge to remove any burrs and then lightly sand the two edges you will be drilling into to.
Now, go find a needle, nail, finely pointed tool, and make a slight indent where you plan to drill. This starter hole will keep your drill bit from dancing across the top of your already too little surface. And the filed down shiny surface that you did during prep will make it easier to see.
Now carefully drill... Note: with super thin drills like a #78 (.016) or #76 (.020), they have a bad habit of breaking and leaving the hardened head behind buried in your work. It normally happens when the slag (whatever drill debris is called) clogs the drill head and as you are turning the drill it gets fractionally bigger and as you turn it more you snap it off... To avoid this, I remove the drill after a couple of turns and clean the slag out and then drill a little more... This is more necessary the deeper you go.
Once you have the first side done, then line up where the second hole should be and do the other side...
When pinning a part, the deeper you can go the better (as the added wire will increase the strength of the repair), but the deeper you go the more chance you will break the drill bit.
After both sides are drilled, glue in your wire...
And now is the time for green stuff... Not only will it help you hide the repair, the sticky nature of it will help hold the part together, because every little bit helps.
If you have a hobby vise, those come in handy, but I wouldn't recommend buying one unless you plan to do a lot of reposing/bashing.
Caz