Scott asks about a veneer cutter:

This tool doesn't look like a saw at all,
more like a slitting device.  The metal
plate on the side looks like it contains
a single-edge razor blade, or something similar,
angled so that the rear end is down and the
front end up.  If this were angled so that the
rear end drooped just the thickness of the
veneer, you should get a nice cut.  The cutter
that is shown does not have the blade registered
against one face of the tool.  If you are cutting
against a batten, you need to allow for this.

The horizontal U shaped metal thingy is a 
fence which gives clearance for the veneer,
useful for edge trimming.  Looks like it can be 
removed for cutting against a batten.

I'd think you could make the handle any shape
you want.  Attach a blade in a mortise on one 
side so that the blade can be rotated to drop 
the rear end of the blade to give a slitting cut. 
Attach the blade with a bolt and wingnut through
the body.  I'd think that one of those utility
knife blades would work well, I think they have
a hole in the middle?
 
The fence could be made from a block of wood with 
a saw kerf for the veneer clearance.

Does any of this make sense?

Ted