Praise be to Allaah.
It is permissible to do tawaaf wearing shoes if they are
clean. The Sunnah is to pray wearing shoe sometimes. If prayer wearing shoes
is valid, then it is even more likely that doing tawaaf and sa‘i in shoes is
also valid. For more information please see the answer to question no.
69793.
It is better not to do tawaaf wearing shoes, so that people
who are careless and who do not take care to avoid najaasah (impurities)
will not follow your example, which would lead to the mosque being
contaminated and made dirty.
The pilgrim may need to do tawaaf and sa‘i wearing shoes
because of injuries to his feet and so on. So there is nothing wrong with
him doing tawaaf in his shoes, after making sure that they are clean,
because the Prophet (blessing and peace of Allah be upon him) said: “When
one of you comes to the mosque, if he sees some dirt on his shoes, let him
wipe them and pray in them.”
Narrated by Abu Dawood (555) and classed as saheeh by Shaykh
al-Albaani (may Allah have mercy on him).
And Allah knows best.