H.W.
One question you asked popped out to me:
"I'm not sure what to do on my part, besides be patient with his stuttering, and try to redirect him to a not so violent path."
I think you have to let your boyfriend and his son's mom come to whatever sort of agreement that they feel works best for their son. That said, one book I would heartily recommend is "How to Talk So Kids Will Listen...and How to Listen So Kids Will Talk" by Faber and Mazlish. This book is a godsend, and the second part of the title, the Listening part, is very important in drawing out children who might be reluctant to share how they are feeling. Being a trustworthy, open listener can be invaluable in your relationship with this little boy.
As to whether or not the Nerf guns should be abolished in the house-- that might be a pretty big battle. I'm coming from a non-violent stance here too-- we have a Zero Guns/Hurting play household. I think it's important, though, to give this little guy some context for this sort of play. Such as "You need to ask a person before you may play 'shooting' with them. Some kids don't want to play like that, and it makes them uncomfortable or upset." I'd also find some non-lifelike targets for the Nerf guns, like crepe paper streamers hung from a doorway. I'm personally not one for kids playing guns, but if they've already been given to him, it might just be more frustrating and confusing for him to take them away.
Lastly, I'd look for opportunities to help him discover the more constructive and nurturing parts of himself. If you have space for gardening, or even caring for the birds in the backyard, this would be lovely. Does he have a pet to care for? Have him become involved in the daily feeding of the cat or dog. Birds need seeds, suet, and water in cold weather, and I'm sure Home Depot or an online source could supply a build-it-yourself birdfeeder. Find an identification card for your local birds. (As I type this, I realize that you are in Nevada, and I have no idea what the weather is like there right now. Sorry.) The point of what I am suggesting is to help build his sense of goodness and worth through developing other areas of competence besides academic pursuits. I don't know what that might look like, but this might also be an area that his father and mother could put their heads together on. In the meantime, you can still have him help with little things like making a meal or a baking something yummy together. It's always a very special thing to help make something the group appreciates, and if it's cookies or something else easily portable, that would be something he could also share with his mom too. He just might feel very proud of himself!
Hope one of these ideas help!
H.