If it's early thirties, it could be good quality wood by today's standards, so go carefully. Try meths to see if it dissolves the existing varnish, you will need to keep it wet for a minute or two before it gets soft. Shellac varnish was used extensively, and we removed the paint from our stairway using meths and wire wool, revarnished, including the hand rails with shellac (french polish) about 15 years ago and it's still shining and it hasn't been re-done since. Modern stuff will be camparitively difficult to remove later.
Wood work used to have the grain painted on to look like oak or elm etc. when it was really pine. They put on a light undercaot and then applied the darker colours on top, and it was near impossible to tell if it was real in some cases.
You could perhaps remove the older wood and take it to someone who does pine stripping. The stripper has the effect of lightening the wood.