Constrained layer damping tape on toroidal transformer?

Is it safe for me to apply constrained layer damping tape (aluminum core) directly to the exterior plastic wrap of a toroidal transformer?  Are the wire wrappings around the core insulated?  
I would like to know why you say not to use a stainless nut, though. I build a lot of stainless parts for race cars and for food and beverage and try not to use stainless nuts on stainless bolts due to galling, but that’s only if they have a decent amount of torque applied to them. For lightly tightened things like a transformer, though, there usually isn’t a galling problem. So, why not use a stainless nut? You could always use a little bit of anti-seize if you’re worried about galling.
Anti-galling compound should work fine...  I'm just nervous about it perishing and being a problem years down the road.

Just for fun, if you have one of those lazer temperature sensing gadgets, its easy enough to see that a ferrous bolt runs considerably hotter than the transformer itself. Its also easy to see that the latter runs cooler once the bolt is replaced.

I ended up wrapping the primary and secondary tap wires of the transformer with a small piece of constrained layer damping tape to great results. Smoother, quieter, more musical yet still dynamic.