You are absolutely correct. I don't know why but that's the way it is. Perhaps it is because the term goes back to before they added the drones, so just refers to the chanter (the pipe you play the tune on). This definitely predates the addition of the drones, as shown by the similar Celtic instrument - the Breton bombard, which is essentially just the chanter. The Bretons also have a one-drone istrument, the binioù kozh. It is singular in French but I cannot find out what it is in Breton. The also have the binioù braz 'pìob mhòr', imported from Scotland. Bombard (left) and binioù kozh
I am afraid I don't know anyone who is in a position to judge a dictionary's accuracy who actually uses either of these dictionaries. I would stick to the two free dictionaries online at https://www.faclair.com/ Am Faclair Beag has some oddities, including a refusal to follow GOC in certain cases, but is generally quite good. Dwelly is generally regarded as the gold standard for 1911 Gaelic. They both tend to list alternatives when they exist, unlike Watson. Dwelly gives only cudthromach, so it was correct. AFB does not even mention cudthromach but has the rather weird habit of redirecting you from spellings it does not accept to ones it does. So in this case, if you search for cudthromach, even when set to 'exact spelling only', it redirects you to cudromach without explaining why.
I mentioned GOC - the Gaelic Orthographic Conventions. This is the accepted definitive list of spellings and it gives only cudromach (in two places). I have never seen cudthromach in any modern document.