"Fully dry. It's almost invisible and very solid. I tried to scratch the coil with my nails, perpendicularily to the wire. Impossible to damage it. I even wonder if it is necessary to put a shrink tube !" - André
I've seen Tesla coil videos where they use epoxy applied with an old credit card here.
If everything is that secure then heatshrink will add another layer of dielectric, raising the self capacitance and likely lowering the self resonance - though all things being equal, making the coils more physically robust is obviously a good move. My educated guess is that the dielectric between windings near to each other is likely more important than the dielectric from the windings to the environment. Of course the coil former itself has a higher dielectric constant than air, as does the insulation on the wire - these things pretty much have to be there for our types of coils but their influences are directionally incorrect. This is why you see critical RF coils which are wound in the air and made of uninsulated wire or tubing.
Probably no need to be alarmed by it all though - the time is ripe for experimentation! I'd be interested in a before and after inductance measurements of (using the exact same coil for all measurements): bare coil vs. varnished coil, bare vs. heatshrink, and bare vs. varnish + heatshrink - but only if that might work out for you, and only if you feel like doing it. The measurement setup has to be fairly physically repeatable though if the results are to be meaningful. If you are using a similar meter to mine, even small changes to the coil positioning can be seen because it operates at resonance like a Theremin. I do measurements with the meter and coil both on top of an empty plastic box.
What spray varnish are you using?
