Well unless his rights are terminated, you will not be able to totally stop visitation. He has a right to see the child. But you can definately get short supervised visits. My strategy in cases like these is to just set up several hoops he has to jump through before he can see the child. Ask that he attend counseling for several months first. Ask that have the visits supervised for 30 minutes and that he drive to a public place.
The court will often order these types of limits on visitation and make him build up to regular visitation. BUt most of the time, the fathers do not manage to clear all the hurdles and the visitation never happens.
I know you said you don't need the child support, but I would also file a Petition for Contempt for the back child support. Ask that he pay the child support, plus additional amounts to make up for the last 4 years. You could contact the prosecutor's office and have him charged with criminal non-support of a child.
Like I said, you can't stop the visits. You can only make it harder for him so that he quits. Child support is not tied to visitation.
The other alternative is to file a Petition for Adoption by your fiance. Then you could ask to terminate the rights of the father, because of parental abandonment
. If he has not seen the child or paid support as you describe, there is a good chance you could have his rights terminated for abandonment. You will definately need a lawyer for this.