There’s no expectation on ATC’s part that a go-around from a visual is flying the missed approach for some uncleared IAP. Doing so will just make things more confusing. Tower will coordinate a hand-off back to approach, but first they have coord on it. If there’s no traffic conflict just ask for pattern. It’s always amazing how many airline pilots are scared of flying visually without someone holding their hand. Look outside, monitor the TCAS, fly the plane until ATC gives what will be a simple instruction, most likely, “fly runway heading, climb to x,000’, approach 126.x.