A better approach is usually to retouch texture and color separately.

For the visible veins, use the Clone Stamp with a very soft brush and sample from pixels right next to the vein. Clone from below/above for horizontal veins, or from the side for vertical veins, so the texture and brightness match. Work carefully around the edges of the iris and eyelids. Doing this on a separate layer can help, and lowering that layer’s opacity can keep the result natural.

If the problem is mainly redness, try a color adjustment instead of painting in Saturation mode. Use Replace Color or Selective Color to target the reds, lowering saturation and increasing luminance until the veins are less noticeable. Then mask or history-brush the correction only into the whites of the eyes.

Avoid over-smoothing: completely vein-free eyes can look unnatural. Usually the most believable retouch is reducing the redness and strongest veins rather than removing every trace.