i'm afraid i don't know the exact leagal answer, but just have this small comment/thing for you to think about.
the ex will always be the son's dad, no matter if he sees him or not. You say he dosen't want "much" to do with him, so presumably he still has something to do with him. (Paying, perhaps?) there is always the chance of a reconcilliation (between son and father), next week, next year, in five years so what would you do then, change the name back? clearly i don't know the circumstances, but it must be confusing for kids to have their names chopped and changed, and really, what does it matter if he still has his dads name after all he is his dad (even if he isn't behaving like one at the moment)? you say the dad wouldn't sign the papers out of spite, but isn't that your motivation for changing the name?
do you truely think it would be better for your son to have his dad out of his life so much, even to the extent of carving his name up, or is it just to make you feel better?
As i said i dont know your circumstances, and you could have a really really good reason (for example having to go into hiding from him) but i just wanted to make you think. You dont mention the age of the son, but maybe he could make his own decision when he is old enough? the problem when parents have spilt acrimoniously is that the slow drip of poison in the childs ear (including name changing) can be damaging long term, in my opinion