Laser treatment
I suspect the tattoos that you have are the self made Indian Ink type. These can be removed quite easily using a tuned laser. I had a 'professional' tattoo removed from my arm and the black outline was by far the first to go. I dont know how much it costs these days but a couple of sessions should do it. I would suggest that you do it now though as it takes about a month to heal and longer for the skin pigment to return.