I reconstruct medieval and Renaissance woodwind instruments, and so squinting at the strange things depicted in paintings like the one you mentioned has become rather a specialty of mine. I’m creating a 3D-printing-optimized, open-source library of rare, historical, and traditional instruments, and although I haven’t gotten around to digitizing this one, I’m quite certain what it is.

Back in the day (and in modern colloquial usage) a whole range of woodwind instruments were referred to as “pipes,” encompassing duct flutes (e.g. whistles and recorders), transverse flutes, and reed instruments. A “piper” might be a player of any one of these (or frequently several), and we see the Pied Piper depicted over the years with a fife, recorder, or (rarely) bagpipes, among other things.

In iconography and paintings across history we find a mix of ordinary instruments depicted inaccurately, and extraordinary instruments depicted accurately. It can often be quite a challenge to determine which category a given example falls into, especially if no other images are available for comparison, and if no writing on the specific instrument is available.

That said, this example is pretty obviously the former - it’s an impossibly skinny shawm, held incorrectly, and played most unusually out of the side of the mouth here.

The shawm is often referred to as a “folk oboe” but in practice the two are almost incomparable. The shawm was the primary “loud” instrument in medieval and Renaissance music aside from conical-bored bagpipes, and by the 1500s had been developed quite a bit, incorporating bore perturbations and acoustics-enhancing elements, like the cylindrical bulge seen near the end. Another interesting bit about the shawm is that it was often used to signal times of day, open municipal functions etc, and the people who performed this function were known as Stadtpfiefer.

This of course gives us a clue the artist didn’t “get” the instrument - the players lower hand is below the bulge, where no playable toneholes or keys were ever placed, and his grip would not allow him to move his top hand fingers effectively. If the instrument depicted even played, it would only function as a single-note signaling device.

If you go looking for more historical instrument IDs, Praetorius’ Syntagma Musicum is pretty much the dictionary for old European instruments. Some of his drawings are exceptionally accurate - my friend who reconstructed a sort of Viennese smallpipe found it was accurate to just a few millimeters. Other bagpipes, however, seem compressed or to have drones in lengths incompatible with pleasing music, so even this must be taken with a substantial quantity of sodium (I prefer MSG).