Both are equally valid. Choose wheelchair for mobility or health concerns, walking if physically able for the full worship experience.
طواف by wheelchair is completely valid according to all four schools. نبی کریم himself performed his Farewell طواف while riding a camel. The choice should be based purely on physical capability without spiritual concern.
Choose wheelchair if you have mobility limitations, cardiovascular or respiratory conditions, are elderly and concerned about crowd pressure, recently recovered from illness, or are pregnant. There is no shame in using a wheelchair.
Options: rent a manual wheelchair with a companion pushing, hire a professional pusher (SAR 50-200), or rent an electric wheelchair for independence. Wheelchair طواف is typically on upper floors with wider lanes. Walking طواف provides the full physical worship experience and is مستحب for the physically able.
Source: Ibn Qudamah, Al-Mughni; Imam al-Nawawi, Al-Majmu'