Performing السعي between الصفا and المروةh while riding in a wheelchair, mobility scooter, or being carried is جائز and valid عند all four schools of jurisprudence. This ruling applies to anyone with a genuine need — the elderly, those with disabilities, those who are ill, and anyone who cannot walk the distance (which is approximately 3.15 km for seven laps). الشيخ ابن باز explicitly stated that السعي performed while riding is valid for those with a legitimate excuse.
The evidence for this ruling is strong. The Shafi'i school, in particular, holds that السعي while riding is جائز even without an excuse, though walking is more virtuous for those who are able. This is based on the fact that النبي (صلى الله عليه وسلم) performed his Farewell الحج rites while riding, and the general principle that the form of locomotion does not affect the validity of the rite. ابن عثيمين confirmed that the الحاج on a wheelchair or scooter earns the same reward as one who walks, and may even earn additional reward due to their patience with their condition.
Practically, the Mas'a (السعي corridor) in المسجد الحرام has dedicated lanes for wheelchairs and mobility scooters to ensure the safety of both riders and pedestrians. The الحاج being pushed in a wheelchair should face the direction of movement and ensure all seven complete laps are performed — starting at الصفا and ending at المروةh. The person pushing the wheelchair may intend their effort as an act of worship and assistance.