If I file for child support will the father get awarded visitation?

I have a 6 year old child. The child was born in Missouri and shortly after, his father (we are not married) moved to Texas. He acknowledges that he is the father and his name is on the birth certificate. He is not paying court ordered child support. He gives a little money (less than $50 and month) and rarely calls or comes to visit the child. I have asked him to call and visit more often and a few years back even offered him to come get the child to stay with him in Texas for a few weeks. He declined, sighting money issues, but it takes no money to call his child. I even suggested Skype and we did it once (initiated by me) but he hasn’t Skyped ever since. The point is, although he doesn’t and never has denied that the child is his, he takes no interest in his life. My son sadly said to me one day, “I forgot what my daddy looks like.” I have pictures for him to see of course but he says, “That’s just a picture.” The one time a year he does see his father is so traumatic because my son is even more sad and depressed than before the visit. I say all this to ask: should I file for child support? I’m single and living on a teacher’s salary and I feel I shouldn’t have to provide for this child on my own. I would have filed long ago but the only thing that stops me is fact that his father would definitely file for custody and/or visitation. I know this because he told me if I ever filed for child support he would file too. Considering the way he treats my son during his short and infrequent visits it would break my heart to know that he has to go stay all the way in Texas with someone who acts like they don’t like or care about him, father or not. I wouldn’t mind him going to see his father but over the past 6 years he has made it perfectly clear he doesn’t care about him and would only go through with visitation out of spite. So should I file in order to get more money for my son and risk the chance of his father being awarded visitation or should I just leave it alone? I live in Missouri.