Gentle controlled exposure is usually how phobias go from what little I know about them. The dart thing might seem scary, but it gives you the power to make the fear trigger so it's supposed to help you feel confident over time that "it's not so scary" when it might happen outside of your control.

That said, if you are very uncomfortable with this you could ask him if there's any other baby steps you could try first. An idea I have is that maybe he could have you blow up a balloon and let the air out, no popping involved, then if that goes well visit the dart thing again.