My dispenser lists for Paragon Needle 6 shuttle 5.
For Davis it has Davis New needle 10 shuttle 9, Davis rotary needle 6, Davis old style needle 20.
On this dispenser a 15x1 is Boye #16 needle.
On the chart at the top the needles 6 and 16 are almost identical, will post a picture when I can, so maybe a 15x1 works just fine?