Will tattoo removal warp the ones around it?

Once I get my real Problem Tattoo removed, I'm considering moving on to my sleeve and getting rid of the ones I don't like. However, there are some there that I absolutely love.

Will the healing process or removal itself warp the ones I like, especially if they're close to or even touching others that I want removed?

I know the skin swells and heals and whatnot, so I'm wondering if that would affect the tattoos near it, I'm thinking someone on here has been in this situation before and might have insight. Of course I know everyone is different, just looking for an idea. Thanks!