Chrysostom says that St. Paul pardoned the penitent not for the sake of the local authority but "according to [the will of] God, or unto the glory of Christ". (
Homily 4 on Second Corinthians)
This indicates that St. John had the correct understanding, that the "prosopos" here means not merely presence of Christ but also a transmission of His will.
I think we would assume that it was in accord with Christ's will certainly but that is a side point, the question at hand is whether “prosopon”, often translated “person” at 2 Cor. 2:10, means something other than “presence”.
And to this question by what has been presented herein the answer is ‘No’, “presence” or “in front of” or “in the sight of” or “face” best sums up the meaning of “prosopon” and not something like “acting in the person of” or something similar.