Can I have the tattooed portion of my nipple skin removed instead of undergoing tattoo removal? (photos)

Thank you for sharing your question and photographs.  Based on the relative size of the tattoos I think it imprudent to pursue removal as it would lead to a significant cosmetic deformity.  

The difference in outer and inner skin diameters once the tattoo is removed as you conceive it (a donut shaped resection of skin) will lead to extraordinary pleating of skin, flattening of the breast mound, and thickened scarring. 

based on the photos a periareolar mastopexy could remove the tattoo outside the areola but the radial lines inside the areola wont be removed. a tattoo laser could be used on these lines after the bulk is excised