Hi BW, and welcome to TP!
I was going to just say what the short answer to your question is, but then I realised I wasn't quite sure! So here's the not-so-short thinking-out-loud version. Hope it makes sense.
Firstly, perspective isn't really about the lens. It's about the relationship between the different objects in your image, and how far they are away from the camera.
If you want to take a head-and-shoulders portrait using a 10mm ultra-wide-angle lens, you have to be very very close to the subject in order to frame it properly. The lens will be only a few centimetres from their nose. At this distance, other features of their face (eyes, ears, chin etc.) will be a few centimetres further away, but in proportional terms that's a lot - maybe two or three times further away. That's why you get such an exaggerated perspective, with the nose looking so large.
If you want to take a head-and-shoulders portrait with a 600mm super-telephoto lens, you need to be a long long way away from the subject in order to frame it properly - maybe 30 meters or so. At this distance, the other features of their face (eyes, ears, chin etc.) will still be those same few centimetres further away, but in proportional terms that's very little - maybe 0.1% further away. That's why you get such an flattened perspective.
But the difference between these two cases isn't the lens - it's the distance to the subject. If you had the subject 30 metres away and took the photo with the 10mm lens, they'd be very very small in the middle of the picture. But if you enlarged it a lot you'd get essentially the same effect as with the 600mm lens, because their nose would only be 0.1% closer to the camera rather than half the distance.
OK so far?
So ... here's the short answer. (And it's not the one I was expecting!) If you use a 50mm lens on a full-frame camera for a portrait, then you should use a 30mm lens on a camera with an APS-C sensor. Why? Because the field of view is the same, and therefore the distance to the subject is the same in order to achieve the same composition, and it's the distance to the subject which determines whether or not the perspective is flattering.
(For what it's worth, I think a slightly longer lens is better anyway. I'd prefer 85-135mm on a full-frame camera, and therefore 50-80mm on a 1.6x crop sensor. But that's just a matter of taste.)
If anybody else is reading this, please feel free to comment. As you can see, I'm not 100% sure of the ground on which I'm standing. (But don't just tell me I'm wrong - tell me why I'm wrong!)
EDIT: Canon Bob hadn't posted when I started my reply ... I was distracted by something in the middle of writing it!