What's a good (non surgical) method or cream to get rid of or diminish thread veins on the face?

No. Thermocoagulation is a good method, and you may look into www.Veinwave for more information. Some use sclerotherapy, and others use laser, but there is no magic cream to apply to get rid of the facial veins.
None. You may hide these veins with make-up but laser treatments to these areas will give the best results in our hands.

Related Questions

Can you get rid of red face thread veins without surgery?

RF or sclerotherapy. Radiofrequency microcurrent delivered via thin wire touching the red facial veins causes heat, closing them nicely. Sclerotherapy injections work also for larger veins. The tiny blush veins of rosacea respond well to intense pulsed light treatments due to the larger area of involvement and the larger footprint of these devices. Read more...
Light vein therapy. Intense pulsed light (photofacial) can close tiny red facial veins. Multiple sessions are needed. See a physician first to rule out rosacea. It also responds, but additional recommendations are helpful. Use adequate sunscreen to reduce sun damage (veins) on the face. Other methods are radiofrequency needle or sclerotherapy injections. Read more...