I think a old wood won't shrink and swell anymore

Exactly - the wall paper is not on the wood. It is applied to whatever base you decide and fitted into the back. This makes it easy to change if you wish!

I came here to make the same suggestion as Sheeisback. Wallpaper in general is a terrible hassle to remove. Certainly it will ruin the finish. Using foamcore will allow you to easily change the paper in the future.

A piece of lovely fabric glued to foam core would work just fine and you could change it any time your fancied a new look.

I would worry more about a bleed from the finish of the wood through the wallpaper if applied with moisture. I strongly suggest either adhering the paper to foam core board or using double sided tape to secure the wallpaper’s edges to the furniture. But this might not work if your application requires a seam. Good luck!

If you don't already have the wallpaper chosen, you could do this: chasing (wall)paper

An easier way to apply fabric to the back of cabinets and still have it removable (and washable) is to hang it with starch. Technique is explained here.

I hung fabric on the back of my china cabinet with double sided tape intending to do something better in the future...six months later it is still there...maybe I'll check out the ideas mentioned above. But I do like the change....china cabinet is a dark cherry and the fabric nicely brightens things up.

BTW old wood does the same as new wood it expands and contracts . As for wall paper the best is the foam board idea.

Use liner paper first. Then there are no problems. Go for it.