In fact the vast majority of Venetian trade beads I've collected and handled have nominal 2 mm holes, with a range of maybe 1.8 - 2.2 mm. I can string a large percentage of Venetian beads on 2 mm cord, and most of the rest on 1.5 - 1.8 mm cord. With exceptions of course.

I don't have a huge amount of experience with ancient glass beads from the Islamic era, but the ones I have seen and collected have larger holes, 3-4 mm and sometimes much larger, even on small diameter beads. And most of the time the holes are noticeably tapered. I presume the tapering was required to get the beads off the mandrels.

Maybe some others can chime in on the hole size / shape details on ancients.