Not sure of your decor but for me with cats, a performance velvet chair they don’t bother with.

We had cats that lived to sit on the dining room chairs too. They barfed on them, and left their hair there to get stuck on our clothes. We tried a few approaches. One was washable slip covers work when we didn't have company. The opposite would have been ok, but our most frequent company was allergic to cats. They are the main reason we selected leather furniture for our living room. That was a happy accident, because I love leather now. Googling "leather dining room chairs" got me some nice pictures that made me feel they would work but would look very masculine and English castle. I also googled "rattan" and saw some chairs that looked refined enough to bring inside, That's what we have now and I don't think the cats liked sitting on them, but we do. That could look British Colonial or tropical, especially with your teak table. Also remember you can mix styles and materials with one style at the ends of the table and a different style on the sides. That's always ok and is encouraged currently. The last thing I want to say to give you options is that, after the kids flew the nest and the last of our cats died, I took all the chairs to a place that refinishes furniture. They replaced the apholstery and refinished the wood bits where the kids had banged them against the metal table legs. I was amazed at how economical it was. I am far more willing to have them reapholstered just to suit the decor. And I am looking forward to having them refinish other pieces, wood and apholstery. I would encourage you not to wait until you have no cats; do it now. Whatever you get, get slipcovers to protect them between company. That way you can enjoy both and not have as much stress. We no longer have cats. I had two batches. The first batch never barfed or did any nasty thing where they shouldn't. The next batch made such a constant mess I will never take the chance again, because I don't know why.