If your veneer is complete, it’s a pleasant job to refinish. A screwdriver to take the trim off, a flat workspace (kitchen counter), some decent Matt varnish and some very fine wire wool. Start with the wool to get the old stuff off first trying not to scrub away the veneer, then do a couple of layers of the varnish, rub down with the wool to flat and repeat...
Nice job over a few evenings with a glass of wine. Allegedly