Is it likely that there is lead in the varnish of my old 1930's hardwood floor?
This page from Stanford University states:


  Presume all paints and varnishes applied before 1980 contain lead including finishes on old toys, furniture and playground equipment.


Therefore you should take precautions when removing the old material.

However, most of the risk from lead is due to the long term exposure to the paint, so the precautions you have been taking should be adequate.