Since your mole is almost flesh colored, then just shaving it flat under local is simple and easy but has a 50% chance of regrowing. Excising it under local will leave an almost inperceivable mark since this area of the eyelid heals so beautifully on its own and then there is no chance of recurrance.
You need to see an expert in cosmetic mole removal who is experienced in removing growths from the face. There is always a risk for scar, recurrence, pigment changes (darker/lighter/red) in the area treated, and possible need for additional procedures. But an expert should be able to remove the moles like the one in your posted photo with minimal scarring and an appearance more pleasing than currently. Importantly, my patients find that if the mole area becomes flat, rather than raised, even a small scar is a remarkable improvement overall. Always you need to be diligent about avoiding the sun / proper use of sunblock for about 6 months after removal for the best results. Your mole requires a surgeon, not laser or freezing or any other method if you want the best outcome. Please seek out a board certified, fellowship trained Oculofacial Plastic Surgeon or other doctor with extensive expertise in cosmetic facial mole/growth removal. I have had patients travel from around the country in the USA and Europe (I am in Philadelphia) to have me treat them for this kind of challenging removal - especially after they were turned away by dermatologists, general plastic surgeons, and family doctors. My coordinators can conveniently arrange such a visit. I have removed thousands of moles from around people's faces throughout my career and each presents its own challenges, risks for scar, etc. You can review my photos to explore your options -- all my results shown are unretouched, unphotoshopped photos! Costs can be reviewed on my website or with my coordinators. Mole removal is cosmetic surgery and not covered under any health insurance unless the growths are cancerous. Best of luck in your search. Damon B. Chandler, MD Harvard-Penn Trained Oculofacial Plastic Surgeon