Bob Flexner says, "A wax finish is the closest thing you can get to no finish at all." But you know this now.

In addition the the stain you used has a minimal amount of some finish (varnish, probably if from a big box store) to act as a binder to hold the powdered pigment in place until coated with a film-forming finish. If it's a "natural" stain, then it has no pigment and is just a thinned binder. I am not sure why they even sell this except as a thinning agent for the rest of the stains in the line (or to get you to buy yet another product).

Mineral spirits (paint thinner) or naphtha can remove some of the wax as they are a solvent for it. The difference between them is naphtha is a step higher on on the fractional distillation of petroleum, so it is less oily and evaporates faster. Not a big concern. Use clean rags and move to a fresh surface frequently, or use paper blue shop towels on a roll. You could also use lacquer thinner that has a slightly higher solvency factor.

After that, you can use a wiping varnish. You could also use an oil-varnish blend, but that will be less protective and an "in the wood finish" (no appreciable film build) You are not likely to find any product labeled as such, though. See the link. Either is about a foolproof a finish as you can get as long as you don't apply too thickly.

Here is a link that might be useful: Facts about oil finishes