What should be done first with Hand Rejuvenation, remove veins or fat transfer?

I am embarrassed by how creepy my hands look. I had veins removed from my other hand. It helped but not enough. I have an appointment for vein removal for this hand in a week. Will removing the veins compromise the fat from taking having less of a blood supply if done first? My concerns are I don't have much fat. I had 2 fat transfers to other locations already and have silicone in my lower body... so maybe the fat won't be enough to cover the veins? I would appreciate your experience!