It would be preferable to use any cleanser for 2-3 days. Also, it depends on type of peel that you have done.
Best advice to follow post procedure is:
1. Strict sunprotection : apply sunscreen regularly
2: cover your face while going out in sun
3. Avoid cosmetics and make up for 5-7 days
4. Avoid spa, sauna, facial, massage for 5-7 days
5. Avoid harsh facial cleansers for 5 days atleast . If needed, you can use mild cleansers like cetaphil if needed