That could be one possible solution, but some questions arise. Basically the die air pin should be long enough to reach the water overflow hole on cooling bath. Running plastic tube then seals the pin from water. What if tube breaks down for some reason and water flows into a die head. A huge...
Having 20y experience in making small dia tubes of various materials using "free extrusion" technique. Recently met a challange: to make a HDPE tube 6mm OD, 5mm ID on 38mm (1.5") extruder with flex PVC screw. Though screw seems to handle the material, thin wall collapses in cold water bath. Air...