Dr. Rif`at Fawzi, former professor of Shari`ah at Cairo Univ. , states: “First of all, we ask Allah Almighty to grant you Hajj mabrur and happiness in this worldly life and in the Hereafter. Hajjs/pilgrims are permitted to enter the mosque with the shoes as long as we are sure it is pure. Also, during tawaf we can have a rest from time to time while performing it.
Allah Almighty knows best.