As /u/sticky-bit observes, the Geneva Convention was in force by then. The first Geneva Convention was in 1864, and dealt with the treatment of sick and wounded on the battlefield—among other things, it established the red cross symbol. The second was in 1906, and addressed sick and wounded at sea. Then in 1931, the third Geneva Convention addressed the treatment of prisoners of.

I'm really not sure why it's so commonly believed that the fourth treaty of 1949 was the first, but it wasn't. The fourth, by the way, was a general extension of the content of the first three, and also included provisions for civilians.

At any rate, as of 1931, what the Conventions essentially said was that marked ambulances and hospitals were to be considered neutral unless occupied by military forces.

I don't see anything at all in there about protections even for military medics, let alone musicians. And frankly, protection for musicians would have been absurd—like protection for radio operators today. Don't forget that the use of bugles, drums, and bagpipes for command and control on the battlefield was within living memory.

You know the "Charge" ditty you hear at American sporting events? It's called that because it was originally an American military signal to, well, charge.

Anyway, the Geneva Conventions weren't the only source of war crime law at the time, and not the one where you'd most likely see a proscription on killing musicians or (actual) non-combatants on the field. That would be the Hague Conventions of 1899 and 1907. While the Geneva Conventions covered the treatment of prisoners and enemy wounded, the Hague Conventions rather more directly concerned themselves with the actual fighting of wars.

As to what they say about whom you can kill, they basically say you can't bombard undefended cities, or take reprisals against civilians in occupied territory. (With regard to prisoners and wounded, they simply say the Geneva Convention of 1864 is in effect.) I can't find any specific protection mentioned for anyone physically on a battlefield; except that the Geneva protection for ambulances were implicitly reaffirmed. And at any rate, when they were signed musicians were still in very active use for command and control.

You can find the text of all of these treaties, as well as other important law-of-war treaties (like the Paris Declaration banning privateers, or the Kellogg-Briand pact outlawing, um, war itself) here.