The facial deformations you are worried about are due to perspective distortion. Perspective is determined by one thing and one thing only: subject distance.

Here's an example of focal length distortion on a full-frame sensor:

That really is an example of how changing the subject distance to frame the same subject with different focal length lenses affects the perspective. To get the subject (roughly) the same size in each image required very different shooting distances for the 20mm lens and the 200mm lens. The 20mm shot was probably taken less that a foot away from the tip of the subject's nose. The 200mm shot was probably taken from around 10 feet (if the lens in question is an "honest" 200mm at short focus distances).

In the first case (20mm) the subject's ears were nearly twice as far from the camera as the subject's nose. In the last case (200mm), the distances between the camera and the nose on the one hand and the camera and the ears on the other was probably less than 10 percent.

If you take a picture with a 50mm lens on a FF camera from a distance of 10 feet and also take a picture with a 30-35mm lens on an APS-C camera from a distance of 10 feet both pictures will have the same perspective and framing (allowing for the rounding of focal lengths - a 50mm lens may be anywhere from about 46-53mm in actual focal length and most other lenses are also usually rounded to the nearest common focal length).

The focal length of a 35mm lens is always 35mm. A 35mm FX lens and a 35mm DX lens will both provide the same field of view on a camera with DX sensor (Again, allowing for that pesky rounding - all 35mm lenses aren't exactly 35mm. Some are 37mm, others might be 33mm).

The only reason we use crop factors is to compare the angle of view (AoV) of lenses used on cameras with smaller sensors to the focal length needed to obtain the same angle of view on a full frame body. When comparing the AoV of a 35mm DX lens or 35mm FX lens used on a DX body to the focal length needed for the same FoV on an FX camera both lenses need to be multiplied by the DX crop factor.