Should I give into my OCD and do a Clean Hands run? on my first run?

I would have to start the game over because I got 1 kill, probably by rats, on the Prologue. I know this is a subjective question, but I feel it will itch in my brain the WHOLE time I'm playing. So what do you think, should I just start over and be careful? Also, is it extremely difficult with the rats? Idk if I will even be as fun replaying missions over and over if needed.