Hi, Dry Ice is not nearly as cold as LN2, but it is still much colder than a normal freezer. It might be cold enough for your project.
Unlike the author of that video, do not handle dry ice with your fingers. There is something fishy going on in that video - dry ice will stick to your fingers and cause nearly instant frost bite. He was handling it with his fingers - just crazy. That would only be at all feasible if the dry ice had become coated by condensation and frozen it, providing some insulation.
Your parts are small enough that you could just stick them in a cooler on top of the dry ice - skip the alcohol - until you are finished with the machining.
