Many years ago I took the brass metal core out of a discarded tire stem. I cut off and then burned the rubber off with a torch. I then soldered a piece of brass tubing into the non threaded end. Been using it for 35 years.

Another option is to get a piece of tubing that will slide over the ball needle threads and a 4mm Festo straight fitting like a coupler. Then hysol the tube over the ball needle and festo fitting to hold them together. When cured screw in the needle base to the pump and attach 4mm tubing to the Festo fitting.

Lot of other ways also.