Hand function is based on muscular and neurologic innervation and properly functioning arteries suppled in a duplicate way by the radial and ulnar arteries. Most people have a complete arch where the 2 arteries cross each other and can take over for another. The deep veins of the hand are critical but are not treated by sclerotherapy.What you see visually on the hands are the superficial dorsal veins and treating them by microphlebectomy or sclerotherapy or a combination of BOTH will NOT affect hand function.
The treatment of hand veins is certainly only a cosmetic issue although I have had a massage therapist whose abnormal veins on her thumb interfered with her work. I have over the last 15 years treated many hand veins with excellent cosmetic results and no functional loss. I use sclerotherapy for the smaller veins and laser ablation for the larger cord like veins. Both forms of treatment work very well, are well tolerated and have high patient satisfaction.