I think it's generally fine to leave it overnight if the syringe is sealed well. I sterilize a plastic eyeglass case and use that whenever I need to prefill.
My mother has been thinking about doing daily GHK injections but doesn't want to handle drawing from the vial because of her poor depth perception. Would it cause any sterility problems if I drew up her dose the night before and left the cap on the syringe so she can just grab it from the mini fridge in the morning?