Also, there is CaledonianClassic Car Hire but they are further away down north of Edinburgh http://www.caledonianclassics.co.uk/location.asp but I suppose either could you mean you can take in a nice scenic drive up to the Orkneys.
No knowledge of either but others may have experience of them. Other people onTM seem to speak highly of Revolutions on here.
Revolutions is your best bet for Morgan hire in Scotland. The Scottish Morgan Club visited Orkney for a long weekend in May 2013 and it was a very "Morgan Friendly" location - I counted only one pothole during our time there! We were invited to join the local classic car club for their tour of the island on the Sunday and, as it is an annual event, you might find that it is taking place while you are there. http://www.orkneycommunities.co.uk/ORKNEYVINTAGECLUB/