pictures of Ib Kofoeld Larsen chair  

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Apart from some dust, the...
Apart from some dust, the finish seen in the pictures does not look too bad? While Selig's imported Danish chairs were also made of natural teak and walnut in an oil finish, your chair appears to be one of the many that were made of beech, which is a blond wood, and has been stained a walnut color by the factory, and then given a protective varnish finish. Doing a full refinish on these chairs is quite challenging, especially if it involves removing the varnish coat and having to re-do the stain. Even with all of the old finish removed, beech can be quite difficult to stain evenly, and might require some specialized processes, like the use of pre-stain conditioners, or non-pigmented dyes. I have had some experience re-doing an armrest on a similar Selig chair, and I had a host of problems with it.

pictures of Kofoeld Larsen chair
Thanks for the info. I think refinishing for me is out of the question. Thanks Barry

what's your question then,...
what's your question then, barry?
I myself would just use a conditioner to feed the wood again and give back it's shine or glow.

Wax it!
Hi. It's hard to tell the condition from the photos. If you don't want to tackle a refinish job I would wax it with a paste wax.
First clean the wood with mineral spirits and a soft rag or a white scotch brite pad. This will remove all the grime and built up wax. Thoroughly wipe it down and allow to dry. Get yourself some colored past wax that is close to the wood's color. Most likely a dark walnut would be fine. It doesn't need to match exactly.
I like the brand Black Bison.
Take an old t-shirt and make a square about 8x8 inches. Place a glob of wax in the center of the cloth and wrap making a ball. Tap on your palm to allow the wax to penetrate the cloth. Applying the wax this way gives you a more consistent thickness.
Apply the wax to the finish like waxing a car. The color will penetrate any minor nicks and color them while applying a protective coating to the finish and raising the sheen. Wipe the wax off once it begins to haze.
A second coat may be necessary.
Be careful not to get the wax on your upholstery as it may stain. You may be better off removing the seat or cushions if they are loose.
I think you will be suprised with the results 🙂