There does not seem to be a difference between permanent and semi-permanent dyes regarding chatzitzah. Most hair dyes are absorbed into the hair and do not leave a tangible residue. Therefore they are not considered a chatzitzah.

You should just take care that your dye job is well maintained prior to immersion and you do not have noticeable roots/patches that need to be touched up, and with which you would be uncomfortable being seen in public.