Passepartout can visit the Banganga temple in the city, where the priest and the believers can divest the valet of his shoes and hat, as in the book. In the Hanging Gardens, Passepartout might chance at the sign of the Artificer's Guild on the door of a mansion.
If Passepartout has an Artificer's Medallion in his possession when he explores and visits the Artificer's Tower he can open a route to Agra via Artificer's Airship (with the right conversation choices). Note that they take the medallion.
It is very easy for Passepartout to loose both shoes and hat while exploring, but doesn't seem to change either the amount of money he has or what is in the suitcase.