I frequently treat hand veins both with sclerotherapy and endovenous laser ablation with very excellent and cosmetically acceptable results. There is also minimum discomfort and associated downtime. If the veins are treated by either method nothing will change with the blood flow in the hand. There are plenty of collateral veins to pick up the flow just as in the legs after sclerotherapy and laser treatments.
to your heart normally, just not throught the veins being treated. blood return will be unaffected by treating large superficial veins. sclerotherapy is very useful to treat these veins as long as an experienced physician does this for you. Cheers