My question is it just so happens I finished my last non-speed run with the Chicago sweeper in my inventory I want to do my speed run with the TMP and the riot shotgun and fighting knife none of which are in my inventory is it going to reject my run if I just do not use the sweeper at all make it to the first typewriter store it and grab the weapons that I want out or do I need to just do another whole run and make sure I end it with everything that I want for my speedrun in place before starting? Also just to make sure are the cat ears and actually armor allowed in the any percent New game Plus category

Fairly sure you can take them out at the typewriter (as long as you're mid-chapter and only taking stuff out), but it's definitely better to just run through the whole game and finish with your desired loadout. That way you won't need to do it everytime

It's also helpful to make a save at the final merchant in case you need to make changes down the line.

And yes, you can use cat ears and armor ashley in Any% NG+