For a once again run to count is it simply just a case of unequiping the weapons I have unlocked from previous runs.

Jill is auto equipped with a rocket launcher now.

Thanks just didn't wanna break any rules by having it equipped.

Appreciate the response

Wait, I was told elsewhere that the weapons you unlock are allowed in New Game + runs, so are you not actually allowed to use the rocket launcher/samurai edge?

I believe he is clarifying the allowance of selecting "once again" to count for a new game run. Maybe for skin preference? But in your case, NG+ still allows bang bang shooty time with the launcher.