Is it possible to have chocolate chunks in ice cream that aren't waxy?
I use dark chocolate chips (Whole Foods brand, vegan) when I make my own ice cream, and have not encountered any waxy texture. I can vouch for that but you can probably experiment with your favorite chocolate chips.

Somewhat OT but making mint ice cream isn't too hard if you have an ice cream maker, just follow the instructions for vanilla but use mint extract instead. Then add the chips when the ice cream is about 5 minutes away from being finished in the ice cream maker.