I really like the Formby's products for light stripping and refinishing. They dissolve the finish and leave the stain and character intact. In this case, you could just wipe down the area you want to finish with acetone or xylene solvent to soften and remove loose finish. If the chairs are less than 20 years old, refinish with clear spray lacquer for the clearest finish. Older chairs should be varnished (tends to darken). Polyurthanes are a very tough and resiliant finish and a good option but will not finish quite as smooth as the lacquers.