If there are skin lesions and this lesions is sporadic I guess the answer will be slightly yes but we have to notice that the materials of Stethoscopes are plastic and stainless steel so the ability to carry infectious microbes is very limited
stethoscopes can spread mostly in contagious diseases like FMD in cattle & sheap or strangle disease in horse
Some veterinary hospitals have isolated place for contagious diseases & hospital staff use another stethoscopes that is in isolate section and they don't use this stethoscope for examining another patient