Yes. Red-looking skin tones are usually caused more by white balance, picture profile/rendering, and exposure than by a camera having a dedicated “skin tone” setting.

A few things to try on the A7 III:

• Use a consistent white balance instead of relying on changing light and Auto WB every time. If the light is stable, set Kelvin or use a custom WB from a gray/white reference.
• Shoot RAW if possible. That gives you much more control to fine-tune white balance and tint afterward without degrading the image.
• Check your Creative Style/Picture Profile settings. Some styles can make reds look stronger; a more neutral style is often better for portraits.
• Watch exposure. Slight overexposure or mixed lighting can make skin look overly warm or red.
• Compare in the same lighting. Different brands render color differently, so part of what you’re seeing may simply be Sony’s color response versus Canon’s.

There typically isn’t a simple skin-specific correction in-camera that fixes this universally. The most reliable approach is neutral white balance, a less aggressive picture style, and RAW processing for portraits.