Chuck.......The handles in the first pictures appear to be void of any color? Do they show any wood color at all when they are wet? If you wet a piece of wood with alchohol, water, or anything, it will show the color of the wood if you put a clear finish on them as they are. The pictures in books look like they are light colored. I dont know if thats from color fade over the years or not. If they dont have a color you want, I'd consider staining them first if you want a wood color. Then apply a clear finish. Tung Oil, or an oil finish of anykind is ok, but IMO, takes a long time to dry and is not as durable as some modern clear finishes. Its a matter of opinion, but I'd also use a satin finish product....a tough urethane floor finish, out side door finish, spar varnish, or a bartop finish. The old finishes, varnishes and lacquers, back when that iron was made wont compare to the durability of modern finishes and by sight, no one can tell the difference, IMO.
PS......First time I've ever noticed the word Mould on a waffle iron. Interesting!..especially in light of the spelling of mould versus mold.
