I have never air layered an azalea, I have heard that they will, but never tried. The apex on the clay potted one is not that thick and you can grow one from a cutting to that thickness in two seasons, so I don't think you would be getting anywhere by air layering; unless, you just want to try it out for an experiment. I, like 808 mentioned above, strike all of the cuttings when I trim, you would be surprised how many of them take. The only one that I have not had success with is chojuho.
Concerning the repot, not trying to be snarky, but what is it that makes you think it needs repotting? Just curious. It looks healthy, is the soil draining (when watering, does the water flow through or pool on top?) I see at least one flower bud in the pictures of it (the rest are not close up enough), the picture with your finger in it, the top right, there is a bud.
Instead of a full blown repot, why not take it and plant it in a larger container and let it stretch its legs a bit. You could use a cut down nursery container, an oil drain pan ( I like these), or a terracotta orchid or azalea pot. Just take yours out of its pot, loosen up the roots, put in the larger container and back fill with good soil. Thin out the branches some and wire the ones left to get some movement in them. You will be surprised how much growth it will throw out. After a year or so put it back in a bonsai pot. I could be wrong again those little green thing might not be what I'm thinking they are
I know you are anxious to just in on it, but I think going a bit slower with it and seeing how it responds to different techniques would be better, I would hate for you to loose it by doing too much at once.
John