Cutting on the griddle.

So I make a ton of chicken thighs or breast for meals, and usually being them inside to slice or dice up.

Recently I've been using the scraper which seems to work well if you hit the grain nicely. However, I do notice markings on the griddle from this.

My question is does anybody use a rocking style pizza cutter on their griddle without marking it as roughly? I thought I'd ask before getting one, it seems like it would do a decent job if it stays sharp.

Thanks and grill on!