I have an old pair of ADS that need to be re-finished. They are good structurally, but need to be stripped and sanded then re-stained.
Was there a penetrating oil finish (open grain) or a sealed finish (sealed grain) on those speakers? Run your finger nail edge over the grain to see if it catches on the open grain. Walnut can be finer grained than oak, so look closely. Compare that to some other furniture you have that has a more obviously glossy sealed finish.
If it's open grain, wipe it as clean as you can with a rag dipped in thinner or mineral spirits. Then wipe on a penetrating oil finish such as
Watco Danish Oil, or an equivalent brand. These finishes contain boiled linseed oil or tung oil. It penetrates into the wood and leaves an open grain surface. Use a clean rag or extra-fine (XXXX) steel wool. Get the clear or natural finish. The kind with a dye added will make your speakers darker.
If your speakers have a varnish or lacquer finish, rub with extra-fine steel wool dipped in varnish remover or thinner. Clean up all the dust carefully and apply fresh varnish. I usually thin the varnish in mineral spirits (a 50/50 mix) and wipe it on with a clean rag in thin coats, letting it dry overnight between coats. You can also buy varnish that comes as a gel in the can. It works well and cannot drip or run. Again avoid adding a stain, go for a clear coat. I've had good results with
Bartely's, but there are plenty of others that work well.