After dissolving the finish on the cane, clean it completely and evenly with the lacquer thinner. Let it dry then out of the sun for an hour or so. Longer if yuou used any water in the stripping process (which is un-necessary of course). Then, if you want to stain the cane to match the refinished chair (and Hutch) mix artists raw linseed oil (which you have boiled (just heated to the boiling point of water) in a sauce pan on a hot plate or range. YOu can know if it's reached 212 degrees F by adding a drop of water to the oil (with a finger, shaking the water off; or with and eye dropper, etc.) If the water sizzles it is evaporating, so you know it boiled off. Turn off the heat and let cool for adequate time to be touched. Youo only need to boil as much oil as neededd to stain the cane seat(s). Depends uupon how big the area, and how dried out the cane. Lacquer thinner is very drying. When you have added the color, pigments, and it matches the wood stain areas, apply with a brush, working it into the cane. Only stain the top of the seats. When color is correct, let dry for 48 to 72 hours in a warm, dry area out of direct sunlight. Then apply your own homemade boiled raw linseed oil and beeswax finish. To make, heat raw linseed oil in the top of a double boiler. When a drop of water placed on it boils off, you have non-lead poisonous boiled linseed oil. Before cooling, and with heat still on (heat gradually for both the above processes)add "organic" yellow beeswax pastilles until you have a finish that has the consistency of honey. Turn of heat. When useable, apply to top and bottom of cane. Brush into the cane well. Let dry twenty to 40 minutes. Then wipe off, gently, any excess. Let dry 72 hours. Apply additional coats this way if needed.