It should be clear that being in a state of wudu’ is only required for Tawaf. As for other rituals of Hajj, wudu’ is not required.

Responding to this, Dr. Muzammil H. Siddiqi, stated,

Wudu’ is only required for Tawaf. Therefore, if at any time wudu’ breaks, the pilgrim should stop the Tawaf, make a fresh wudu’, and then resume the Tawaf.
Wudu’ is not necessary for throwing the pebbles even though it is recommended and preferable to have wudu’.