Do you mean the appliques glued to the sides of the drawers like this example?
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The wood appliques would be difficult to repair without the missing pieces. People part out treadle cabinets on Ebay all the time. If you see treadle parts with the same pattern contact the seller even if you don't see exactly what you need. They may have damaged drawers with the parts for your applique that you need, or better yet the correct drawers in good condition. That's the easy route.
After you find a source for the missing pieces it becomes a matter of very carefully taking the pieces you need off. I would try loosening the glue with steam. You can also use a sharp stiff putty knife to help pry them off. Be very careful. They're fragile. Once you get them off cut and splice the replacement pieces into your existing applique. The repairs should blend pretty well. Try to keep sanding to a minimum so the original finish blends better.
If you can get some pictures posted that will help people decide the best course of action.
Rodney