[klondike98]

I'm not certain but your set might be a 60L.  The escutcheon is different than the gallery picture but the 60 series went through a long evolution as seen here in the 1935 (July 1934) and 1936 (June 1935) table models.  Those escutcheon and knobs seem to match your set.

As for the veneer, yes the veneer on the right side panel would need to come off and be replaced.  I'm not the guy to tell you how to do that as I've never done it.  I've only patched small sections.  Read through some of the cabinet restoration threads in the Phorum and you'll get an idea of what the effort will be and some of the techniques people use to strip, tone and lacquer the sets.  Here's just one place to start...Ron's 2018 cabinet work thread.  Here's another by Fred.... and a couple more LINK 1 and LINK2. There are many others that would be good to review I'm sure others will chime in as well.