HelpHow do I use my new legit Steam key with old Banned account?

I just bought a new legit Arma 2: OA Steam key because I want to play the game legitimately, but I want to use my old account. I have Darky's Key Checker, but I am wondering if I take my new key, and put it on my old account, will BattlEye detect it as stolen and ban it, or will it be fine? Because when I check in Darky's Key checker for my key, it still shows the banned one. So, do I need to change it? If so, how should I go about it?

I hope you understand what I am asking, it seems a bit confusing I know. Thanks for any help!