It looks like you're pretty well covered:
British Museum: "Wheelchairs are available free of charge at both entrances. Please contact us before your visit if you would like to ensure that a wheelchair will be available."
Victoria and Albert Museum: "Wheelchairs and walking frames are available at the information desk in the Grand Entrance."
Science Museum: "A limited number of adult and child wheelchairs are available and may either be booked in advance by telephoning 0870 870 4868 or borrowed on the day by asking a member of staff at the Information Desk."
National History Museum: "You can hire wheelchairs for free from the cloakrooms just inside the Exhibition Road entrance, or next to the main toilets behind Hintze Hall."
National Gallery: "Wheelchairs are available at the Getty Entrance on level 0, the Sainsbury Wing cloakroom on level 0 and the Pigott Education Centre (street level)."
National Portrait Gallery: "Additional wheelchairs and seating can be provided. To book a wheelchair in advance of your visit please contact 020 7306 0055, or ask at the Information Desk."
To take public transit while seeing the city overground, bus is the obvious choice. London has a very reliable bus service, and using it routinely works out cheaper overall because of daily capping.
I hope you do your best to maximize wound healing. If you're otherwise fit and healthy, aside from the usual advice, for locomotor injuries I personally recommend taking a silica supplement such as
food grade diatomaceous earth to expedite recovery.