Reference: Fataawa al-Hajj wal-‘Umrah waz-Ziyaarah – Page 78
Question: Is it compulsory to have wudhoo in order to perform the tawaaf and the sa’ee?
Response: Having wudhoo is compulsory for the tawaaf only. As for the sa’ee, then it is better to have wudhoo, however, if not then it is acceptable.