Tung oil would be a fine finish for your sugar packet holder box.
Be sure to securely fasten the base to the top before applying the oil. This will keep the base from cupping when oil is added to the wood.
While I prefer a few coats of spray satin lacquer because it is quick and easy, tung oil will work as well. It is slow drying and be sure there aren’t any puddles of oil in the recesses as it sits to dry.
Please post your finished holder in the My Carvings! forum so everyone can enjoy your work.