I don't like using Pledge to dust with. Can I spritz vinegar on my rag, or just plain water? Will it hurt wood furniture?
I've been dusting with a damp sponge (plain water) for decades and I haven't seen any damage yet. Just wring out your sponge real god so that it's damp, not dripping.
I clean homes for a living. A dear friend informed me to use a micro-fiber cloth. Wet it slightly, then wring it out. It works amazing. (As always, test on a hidden area.)
I use to work for a large furniture store on in the showroom. To properly clean and polish the furniture we used a an even misture of lemon juice and olive oil. It doesn't pentrate the furniture like water might. Since all wood surfaces are different, water may work on some but not on others. Furniture polish is never recommended for cleaning wood.
The key is not to let the wood be wet for very long. You can clear the dust off with a dampish cloth, then follow with a dry cloth to take the water off. You might do an online search for natural ways to keep your wood surfaces oiled, which they do need now and then. My clock repairman used walnut oil.
My dining room table has been cleaned up every night with the damp rag, no matter how gunked-on the food got, like pizza cheese or whatever. About every three months I use oil on it. God bless you!