Assume a mass casualty type situation. Something along the lines of AR-558 with physical wounds ranging from phaser and disruptor hits, to concussions, broken bones, and the like.
Each Chief would be from roughly halfway through the run of their series with whatever knowledge and experience they had at that point. Each would have access to whatever kind of portable medical kit a medical officer of their time would have brought for such a situation. There are no able bodied personnel to help. No they don’t have access to a transporter.
I’ve seen some great answers to the question as asked. I want to also toss the new-Trek engineers in there: Stamets, Billups, Jankom, and Pelia.
Jankom would be awful. Terrible bedside manner and a predilection for percussive maintenance do not make for good medical outcomes.
Billups would likely not do well either. Granted, we don’t know much about him, but it seems like he’s a competent but not outstanding chief engineer (let’s face it, that’s kinda the point of the show).
Stamets would freak. He would repeatedly note that it’s actually his husband who’s the doctor. But he’d probably end up doing a decent job.
Pelia has the distinct advantage of centuries of experience in her favor. It’s entirely possible that she was a doctor at one point.
And, honorable mentions:
Hemmer would probably shock everyone by being amazing at the job. He would probably show some unexpected advantages to being blind as a doctor.
Jett Reno actually did this scenario, in her first episode.