Many schools do look at the waiver process on a case by case basis. While you cannot force your ex to have a relationship or form an emotional bond with your child (there are intact families where children and parents really do not have an emotional bond with one another), your NCP does provide financial support and is known to you and your child and you can contact him if you need to.
You also stated that your child has a relationship, maybe more like an indulgent uncle than father, but a relationship, none the less. There are also many intact families where parents refuse to pay for their children to attend college, especially colleges that cost upwards of 60k/year.
If you already know that your ex will not contribute, apply of you want, but be prepared for the fact that you may not receive a waiver. Have your son apply to schools based on what you know you will be able to pay for college. Again, make sure your son has some financial safeties, along with schools where he can get merit $$.