Correct. It is up to the council to determine the arrangements for appraisal, including which councillors are to carry out the appraisal. The council can decide things like the time and place, or can delegate that to the appraisal panel. The council is the employer - and as usual must act through formal meetings. Provided that was done, and the clerk has been treated reasonably, the appraisal should be perfectly valid.
Of course, there is nothing to stop the clerk from putting forward proposals for the appraisal arrangements in order to assist the council. But the decisions remain the council's.