You're just going to have to test. It's the only way. Keep in mind that dye fades with exposure to light, which will be less of an issue if you only put it on the hull.

However- I'd like to throw into the mix that as you test you may also want to bleach the wood before adding dye. Wood can be bleached, and as a cabinetmaker I've done it several times. The most effective is sodium hydroxide (caustic soda) and hydrogen peroxide as a two-step. Look it up on line. It's pretty cheap. Test all the way- bleach it, then dye it, then glass it.

There is no shame in testing- pros do it all the time.

m