You do not need to use a pumice stone for dry skin on your feet, particularly if using it causes your skin to peel.
However, if you regularly use a pumice stone as part of your usual foot care routine, independent of mikveh, then you should also use it when preparing for mikveh.
While dry feet are not a chatzitzah, you should soak your feet in warm water during your preparation (and/or use moisturizing cream on your feet for a few days prior to mikveh) to soften any hard skin before immersion.