The problem with washing hair on Yom Tov is that you might squeeze out the water from your hair or towel afterwards. Therefore, if you can be careful about this, it is okay to wet and wash your hair on Yom Tov in order to immerse with clean hair.

However, shampooing and scrubbing as usual is likely to produce tangles and is not recommended since on Shabbat or Yom Tov you cannot comb out your hair. Instead, you could pour some diluted shampoo over your hair, without scrubbing, and then just rinse with water, trying to avoid tangles.

There is a difference between what one tries to do lechatchilah for mikveh preparation on a regular weeknight – removing every single knot in the hair with a comb – and what is acceptable when combing is halachically prohibited. For a Yom Tov or Shabbat immersion, it is sufficient to make sure there are no tangles by running through your hair with your fingers.