I don't see the distinction you are making between a walk-in and a scheduled visit. Both would be billed according to the review of systems, history, exam, medical decision making, etc that go into an E/M. Your APPs are medical providers, they can bill their own visits. If they're intended to be brief exams before a full workup by the surgeon, then you'll stick with low level new patient E/M for the clinic, then higher level established when the surgeon does more complex decision making or examination the next day.
From a revenue perspective, you might miss out on some revenue because the after hours clinic won't be doing as full or complex a write up on the initial, but that's the price your surgeon will have to accept for not staying after hours himself. Or he could work with the APPs to improve their E/M game. I don't know the scope of his practice, but I would explore to what extent the APPs can document an initial visit, what sort of review of systems etc they're comfortable doing without the surgeon around. That's not really a documentation or billing question though, that's how they've arranged their medical practice, which is quite outside my purview. If the surgeon doesn't want them doing any treatment plans beyond NSAIDs, that will inform your billing. If he's comfortable with the APPs diagnosing patients and scheduling surgeries, that will inform your billing.
Another point to consider is that new patient E/Ms are justified anytime a new specialty or subspecialty is introduced, eg. a general psychiatrist sees a new patient, then a month later an NP at the same group specializing in childhood bulimia (or whatever - I don't know psych subspecialties) could both be billed as new patient E/M codes, because their medical expertise focuses on separate areas. So what I'm saying, is that if the APPs and the surgeon have different subspecialties, you may be justified in billing two new patient codes. Might be a longshot, not many practices have multiple subspecialties represented on staff. Something to keep in mind though.