I thought about this on the way home, and I think I've come up with a way it would work.
You need the 1/8" plywood from a hobby shop. Find someplace that sells what you need to make flying model airplanes. They'll have it. You'll also need a dowel long enough to completely cover the top edge of the sun visor. Diameter TBD when you get the rest of the assembly put together. And last but not least, you'll need some wood filler epoxy and the veneer you want to use.
It would be best to try this on something sacrificial so you can work the kinks out before you do your actualy visors. You could make a mock-up of the assembly with a stiff wire hanger and a properly sized metal rod of the right length.
First, create the pattern you want for the sun visor on the plywood. Make sure you place the plywood so it covers 1/2 of the rod at the top edge of the visor on both sides. You should make one side of the pattern (it doesn't matter which) about 3/4" larger than the visor along the bottom edge. The other pattern should be the same size as the visor. Use plenty of epoxy to hold the pieces together through the wire frame of the visor. Let it cure overnight or longer to make sure it's set up properly.
Then take the assembly and fill the space between the edge of the smaller pattern and the larger pattern with the wood epoxy. Don't worry about getting it smooth and pretty because you'll be doing some shaping with a sander before you apply the veneer. The left and right sides will show some gaps, and you'll need to fill the gaps with more of the filler. Once you've got that done, set it aside again and let it cure per the directionsx2. You're going to be using more than any wood epoxy manufacturer anticipated, that's the reason for going twice as long as directions. While you're cutting the patterns, be sure to locate and drill the screw hole used to tighten the visor and keep it from flopping up and down.
Then dig out some 80 grit sandpaper and your trusty orbital sander and shape the edges. You're going for a smooth curve down to the bottom edge of the visor. Take this slowly. Better to take longer to shape than to try to do it too fast and have to start over again, but if you do go too deep in a spot you can apply more wood filler epoxy and start again. Once you've got that edge shaped, start on the left and right sides of the visor. Here you're going for right angles and a smooth surface from front to back. Once you've got all three sides done set it aside and start working on the dowel. To find the dowel size, measure the thickness of the assembly at the top edge - the metal rod and both pieces of plywood. Get the dowel size just slightly larger. It's going to wind up being something like 1/2" or 5/8".
Now find the size of the rod. It's going to be something like 1/4". Find out how deep a hole you can drill with your drill press (really, don't try this with a handheld drill) and cut the dowel into pieces just slightly shorter than that. Drill all the dowel pieces, one at a time. You'll wind up with something that looks like a wooden straw. Now cut them in half with your bandsaw. You should be able to use each side of the dowel. Glue the dowel all along the top, so you've got a nice round edge. Sand off the lip with your orbital sander and shape it to smooth.
Now, take your veneer and the contact cement you're using and apply the veneer per directions on the cement. Because you've shaped the bottom edge with smooth curves down to a sharp edge, the veneer shouldn't show any gaps. You'll need to trim the edges flush and apply small pieces of veneer on the right and left sides. If you're like me, match the grain direction and pattern carefully so it looks like a solid piece of wood from all angles. Trim the left and right veneer flush and gently sand the corners with a fine grit paper to meld them together.
Stain and finish with whatever you want, putting on many layers of marine varnish.