Brendan
Welcome to the site. The roll of C. Squadron of the Rhodesia Regiment shows one "259 Tpr. Paterson, J.R." entitled to clasps Relief of Mafeking, Transvaal and Rhodesia on his QSA medal - with there being some question about entitlement to the clasp Orange Free State. There is a marginal entry which states Tpr. Paterson also served with 1st Brabant's Horse. This information comes from the "Relief of Mafeking medal roll" by Stan Kaplan. There might be some additional information on your man on the "Units" part of this site.
Assuming that everything is right with the medal, you might care to carefully clean it - or simply leave alone the patina of time. Don't worry to much about "Ghost Dates".
Regards
IL.