Hi Rhona - I'm not sure if I can help but I'm an American who is currently living in Scotland (about 8 miles from Peterhead!). Have you tried the ScotlandsPeople website? (www.scotlandspeople.gov.uk) If he died in Scotland, there should be a death record for him there. If he did go to America, do you know what state he went to? Let me know if there's anything that I can do from this side of the pond! If you have an address where he was on the 1911 census, I'd be glad to see if the house is still there.
Susan