The pressure on a household waterline (even from a well system) will blow out the seals on the DHA.
You will need to use a submersible pump water system with the DHA.
Simply make a tray on your drill press that has four sides on it and a drain line leading out from one side into a bucket beside the drill press. Have a submersible pump in the bucket with the line leading to the DHA. As you drill, the water will recycle through the bucket and feed back to the DHA.
Remember that there is a difference between volume and pressure. You can reduce the volume of water on a household line, but it will still maintain the same amount of pressure. It's the pressure that blows the seals.
Use a submersible pump