It is customary to prepare oneself for immersion prior to Shabbat, including make-up removal.
However, wiping off makeup is permissible on Shabbat. Water can be used, but it would be best to apply the water directly to the face and then remove with a dry tissue, so as to avoid issues of squeezing water from a wet cloth (s'chitah). Thus, it would be permissible to apply light, easy to remove makeup before Shabbat and wipe it off prior to mikveh. We would suggest doing a trial run a different day of the week to work out any kinks in advance.
Please get back to us with any further questions.