I think that,s what Mart,s proposing...its the easy way...but unless you filled in where the veneer is missing...you would always see the difference...doing it my way..using 2mm ply...is relatively simple...first you would make a template of the back...strong card could be used,once you have cut the template to size,..you would then lay it onto the 2mm ply,...and being 2mm thick..it is easy to cut,..then get yourself a 500ml tin of contact adhesive...do one side at a time...spread the adhesive over the back panel, and over the ply to be used on the back,..leave for the stated time..usually 20mins/30mins...then carefully bring the two together,...then do the other side,...once its done, you can then stain the ply to match the chair,...then use a satin clear varnish....