I just discussed this last week with my colorist (my Mom has a benign brain tumor that will require surgery).
He said the growth only needs to be a 1/4 inch long to dye it. I assume that the hair itself is also an issue for you til it grows out. My suggestions is this: dye the new hair, you will feel better if it 'blends' visually. Then use this time as an excuse to rock scarves and funky hats til it grows to a point you can work with.
Whatever you chose good luck and speedy recovery! And keep up with things nutritionally so your new growth is maximized!
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