At 60 years + old the finish is oil base varnish. Polyurethane is a fairly new finish. Getting a pickled effect will be difficult with the finish on the wood, the new stain will not soak in. Stripping off the varnish is the best way, but it is possible to get the desired effect by applying a pickling stain over the varnish. You will need to experiment to see if the new stain gives you the look you want.
You can try using the deglosser only. The best is Paso but use whatever is available in your area. Sanding is better than a deglosser. Don't worry to much about lead, this mainly applies to old primers and paints, but you can test for lead. Lead test kits are available at your local paint store.