There is only so much restricted time you're given to keep on putting off something that you're going to have to end up doing anyways in the future. You should definitely let your manager know about your stammer. It's nothing to be ashamed of, it's just one of those "things" that's only a small part of you as everyone else has their own insecurities too but it doesn't have to define you unless you allow it. You can be a stutterer but also a very confident person at the same time of not caring about it. If you really are feeling too much intense anxiety from taking part in this project then take care of your mental wellbeing and see what they say but just know that chances are not everyone is gonna make such a huge deal of you stuttering when they should still care of what you're going to say regardless of some blocks here and there!