A natural-looking fix is usually to darken the shiny areas rather than use skin smoothing.

In Lightroom, try a local adjustment first: use a radial or brush-based mask on the shiny parts of the face, then lower Highlights and/or Whites slightly. Small adjustments usually look more realistic than heavy smoothing because they preserve skin texture.

You can also try global or semi-global tonal control if the shine matches the skin tone overall:

• Lower Highlights or Whites for the image.
• In the HSL panel, reduce Luminance for the skin-tone colors to gently darken bright skin areas.

If the shiny spots are truly blown out (clipped highlights with no detail left), Lightroom may only partly recover them. In that case, highlight recovery may help a little, but you may need more targeted retouching such as spot/healing-style corrections for the worst areas.

So: start with a local mask and reduced highlights/whites, use HSL luminance if needed, and avoid relying on skin smoothing alone.