If the stains are now gone, it should be fine. Never use ethanol or similar products on blood stains, that will cause the proteins in the blood to precipitate and cause stains that are almost impossible to remove.
I don’t know if harp strings can handle soap, but in case there is still some visible staining, gently rubbing it with a cloth with a tiny amount of green soap may help. (first wet the cloth, then add some green soap, rinse it with lukewarm water so that most of the soap is gone, then wring it so it’s damp instead of dripping wet). That usually works on clothing / surfaces with older blood stains.