This isn't true. She can. A DNA test will be ordered to make sure he is the father and then it's his choice whether he wants to make his name on the birth certificate or not. Either way he still has to pay.
To the OP - How certain are you that he would follow through on his threats? To be perfectly honest if I thought for a second that there was a chance my ex would kill my kids I'd rather not have him in my or their life. Please remember also that the more a man sees his kids the less child support they have to pay. So you need to consider that he might push the issue of visitation which he will get (supervised at first obviously and if he can prove he's mentally stable and once the child has formed a relationship with him he will be provided unsupervised access).
Just ask yourself.. is the extra money you'd get from child support worth it? Have you considered applying to go into a community/government house? My bestfriend did this while she was studying and she had 2 kids and lived quite comfortably and she also received no child support.
Please don't take this as me saying you shouldn't apply for child support. I think you have every right to receive something from the *******. I'm just telling you to think about the consequences of forcing an obviously bitter man into paying child support. If there's no chance that he'll follow through on his threat then go for your life!