I'm fairly certain the handles were in fact made of wood. Each oar had one long handle, attached to the oar loom by a line of spacers, made like stubby railing stanchions. I think an iron spike was driven through each stanchion, holding the entire assembly together. The stanchions were separated from each other by a distance appropriate for the oarsman to put his hands between them.
Quite a few years ago a fine modeler named (if I remember correctly) P. Heriz-Smith built a model of a Reale, which is (I think) now in the Science Museum, in London. He made the oar handles by gluing a series of extremely thin wood strips to the face of a sheet of wood. He then sliced the whole assembly into narrow strips, thereby producing the "railing" effect that he was looking for. The result was pretty impressive.
Many years ago I bought one of the Heller kits, and tried to figure out an appropriate solution for the oar handle problem. I discovered that the spacing between the "stanchions" on the handles was almost exactly the same as the spacing between the "rungs" of the brass "HO ladder stock" sold in the model railroad department of the hobby shop where I worked. I think it would be possible to make the handles by slicing some of that stuff (assuming it's still available) in half, and gluing the "stanchions" into holes drilled in the oar looms. The unfortunate feature of those oars is that there's so many of them. The task of shaving the phony-looking handles off the Heller parts, then drilling every one of them for the new handles, is not to be taken lightly. After figuring out how to do it, I (as is my wont under such circumstances) got interested in something else. Some day I may tackle that old Heller kit again; I've got one in the attic, and it's a beautiful kit in many ways.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.