I have often times seen vein formation following surgical procedures. This is due to interruption of veins and new vein formation. This is very common. From your picture, you should be a candidate for sclerotherapy. If you have a lot of veins then you may want to see a vein specialist for a venous evaluation before beginning sclerotherapy to see if there is an underlying valve malfunction contributing to the vein formation.
It is possible that the minor skin surgery you had done on the leg contributed to the development of the leg veins. It is likely that those veins would have showed up eventually anyway. From what I can see in the picture, I think you would be a good candidate for sclerotherapy. I would wait until the excision area is completely healed.
Veins that size (although small) don't form that quickly. I am sure they were there and they recently got larger. You need a venous Doppler ultrasound done to make sure there is no clots (very low likelihood) and at the same setting they will measure the sizes of these veins and also measure reflux times at several junctions between superficial and deep veins (groin, behind the knee) and also at the level of the leg (perforator veins). At that point they will formulate a treatment plan and do an ablation procedure (if needed) or just perform ultrasound guided or traditional foam sclerotherapy. Seek a board certified vein specialist from the American Board of Venous and Lymphatic Medicine. Check the American College of Phlebology physician locator site. Read the ebook about venous diseases on the link below. I also recommend that you take a supplement like Varicosamin which contains bioflavonods as a preventive measure.