How do I go about this?

I am married with two sons, ages 8 and nearly 2. They have two different fathers. I was young when I had my older son, so I wasn't married. My older sons dad hasn't had anything to do with him since like fall of 2020, he barely did before then, but now has had no contact whatsoever since then. I also don't get child support, never have, not that I care. It's come to my attention that my son's "dad" wants to sign over his rights. I'm fine with that since my son considers my husband dad, has the last 5 years. I just need to know how to go the best way about it. Do I need a lawyer? I'm located in Arkansas, dad in Tennessee.