The two none omega straps I wear the most on my blue AT are the hirsch lucca and a hirsch performance paul. I think both would look just as good on the golf, although you might opt for the James or another performance option. The lucca is a great strap for omega watches.
Not an identical watch, but close enough to give you an idea. I agree that brown will go well; I got this one from Peter Watchacc:
Thanks It was described as 'honey tan' -I'm really very pleased with it. I got one in the same colour for a JLC:
Get one of the rubber-backed Hirsch performance leather straps, like the James, and put an Omega buckle on it. You can wear it everywhere from the shower to the pool to the dinner table.
I got mine from Otto Frei, but I'm not sure of the best source at the moment. Maybe Omega themselves?