I have some bottles of TransTint, a super-concentrated and expensive dye stain for wood. You mix it with denatured alcohol or water, though I always use alcohol. Just my way, I guess!
If I were looking askance at my wool hat, I would likely go that route. That is what is in the house.
But then, I have never used RIT. Could it be that the answer to all our dyeing needs can be found in this ubiquitous, innocuous and inexpensive substance? Nah. Use the expensive, hard-to-find, esoteric stuff. You'll feel better, and more guy-like.
Killdeer