Methylene blue will not harm the fish. It will increase blood oxygen content, facilitate healing and prevent fungal infections. Neomycin is also an effective antibiotic for this type of wound, it can be purchased as neoplex by seachem to add to the water or as the same OTC triple antibiotic ointment we use on our cuts put directly on the wound. I wouldn't tell you this if it would hurt the fish. The arrow may have introduced bacteria into the wound and you may not see an internal infection until it's too late, an ounce of prevention. Otherwise keep the water as clean as possible and continue with the salt.
I'm just giving advice based on the title of the thread.