Do you know whether it is against OSHA regulations to have a sprayer on a soiled utility sink used for patient care equipment?
Under OSHA, there is no specific prohibition against having a sprayer on a soiled utility sink. Section (d)(2)(xi) of the Bloodborne Pathogens standard, however, requires you to ensure that "all procedures involving blood or other potentially infectious materials shall be performed in such a manner as to minimize splashing, spraying, spattering, and generation of droplets of these substances."
Eliminating the sink sprayer would be a good engineering control to minimize the chance of generating contaminated sprays. You could also accomplish the same thing by prohibiting the use of a sprayer as a work practice control, which you could include in your exposure control plan.