you may also want to look for an airbrush that has a fan tip. airbrushes normally spray a cone of paint. to effectively cover something with dye a fan pattern would be better. I have several Badger Airbrushes, yet another hobby but the Paasche TS is the one that I have for spraying fan patterns. I mainly use it to spray clear on small motorcycle parts.
this kit has all you need.
https://www.paascheairbrush.com/TS-3AS
the smaller 0.25 and 0.38 heads may work with dye with increased dye thinning but the 0.6 fan head should work really well with minimal thinning.
Zonker