Covering tattoo outline

I have a realism tattoo in deep, dark reds. It's about 4 yrs old and the colors have held up nicely. It was my first tattoo and I didn't realize that I needed to specify no outlines when asking for realism. I really like the tattoo but I think it would look even better without the black outline. Could I have just the outline covered with the reds of the tattoo or is this something I just have to live with?
Thanks.