** 1/4 inch saddle valve for water supply, but they say it can't be self tapping. **
That would be "self piercing".
No, that type shouldn't be use. Nor should *any* type of saddle valve be mounted on the underside of a water pipe, only on top of a horizontal pipe or the side of a vertical pipe.
** I initially used a self [piercing] and the pressure at the dispenser is low. **
And that was when new. You should see how the flow gets reduced once the valve starts building up with lime and scale, etc.
** Where can I get a non-self tapping saddle valve? all of the area building centers carry the same products. **
Try an appliance parts supplier or one of the following links: