I would think neutering should help, as hormones won't be raging. it will probaby be about a month before the hormones are cleared. They could still have a fight over a toy-but you will have to stop it, before it escalates. Most dogs always want the toy that another dog has. I have all spayed females and their is an occasional escalation
over a toy, and I just have to stop it. I used to buy 4 of each toy-but that was a waste. They still want the ONE! I would recommend no real bones, or antlers, as that would be more likely to fight over.