For short duration fasts of less than 48 hours, I wouldnt worry about refeeding per se. Refeeding is traditionally focused on the gradual reactivation of your gut and digestive system after an extended time of not processing solid foods.
Instead, for recurring short fasts, your eating strategy would be more focused on having balanced meals in between your fasting days.
The best thing to eat is animal protein since it has all the essential amino acids to repair cells, especially hair follicles. When you get enough animal protein, it signals your body to allow hair and nails to grow in stronger. Red meat is the very best source because it has the correct proportion of amino acids.