I hate to be a wet blanket, but I don't think this will work. I think the hole wil end up off center if it doesn't break through the side of the body. Drill bits, especially fairly small ones like the one needed here, are prone to flexing to find the path of least resistance through the material. And with a wall thickness that small, holding the body in a vise tight enough to keep it from spinning will cause it to flex, which will leave the finished hole out of round. Those are my concerns about this job when using a drill press. I wouldn't attempt it with a handheld drill.
Ideally, this should be done on a lathe, but as mentioned before, soli's are only ~$5.
Keep safe.