Yup, the Infinite Rocket Launcher is a Billy and Rebecca exclusive. Also, you need to complete the game on Normal or higher in under three and a half hours to unlock. RE0 is relatively short, so it shouldn't take to many attempts to speedrun it and get a good time. Good luck!
I don't know if the infinite rocket launcher can be unlocked via Wesker Mode (apparently not), but I can confirm that it can be used in it after being unlocked. I started playing Wesker Mode yesterday, equipped with everything I had previously unlocked in the campaign and Leech Hunter.