If your aircraft is certified in the 'Transport Category' The Cof A remains thus even if you use it 'Privately'. It does not "revert" to the private category at all! unless you subsequently have it re-certified as such. Even in the 'Private' category the work can be done by the aircrafts owner, but technically he is not allowed to disturb any 'Locking Devices' such as locking wire or split pins or tab washers. If he does, he neds a Licensed Aircraft engineer, duly 'Type Rated' on the type, to certify the work carried out. If your wheel has an inner tube, then a new 'creep mark' will have to be painted after the inner tube has been properly positioned and the tyre inflated. Furthermore, if your aircraft is being used for hire and reward, then it may come under the umberella of an 'Approved Aircraft Maintenace Organisation' as part of an AOC (Air Operators Certificate). If this is the case that organisation would have to approve any person (licenced or not) to carry out any task on the aircraft.
Bob.