You'll be fine. I had to do the same with one of my first hens I ever had. Raised them from little chicks and loved them all. Then one turned out to be a horrible bully. She took it to a whole new level. This wasn't pecking order stuff, this was just plain mean bully behavior. I cried when she met her demise. I ate her but I didn't enjoy it and it bothered me badly for a few weeks. I still think of her but I did the right thing and so did you.
