The only issue I see with wood, is the fact that moisture might soak into it then get moldy, that and some strong flavors may stay in the wood making other flavors less desirable. Unless you seal the inside with a good sealer or some sort of finish.
Might want to try a salad bowl finish (can get it at woodworking supply places), that would help prevent it from soaking up moisture and it is food safe. You could just soak the whole drip tip in salad bowl finish for awhile, then blow out the excess from the inside, and wipe off the outside, let dry for a couple days and you should be good to go.