The 82nd Airborne Division has a chorus group that travels and sings but does not have a rifle team. The US Army Reserve has several bands as well. The Army recognizes band members by MOS. Previously, each instrument was a separate Military Occupational Specialty. Currently, 42R is the Band MOS and each instrument is an ASI (Additional Skill Identifier.)
There is no MOS or ASI for marksmanship instructor in the US Army. There isn't even any specified, published skill requirement to teach (or attempt to teach) marksmanship to Soldiers.