Just because someone is behind in child support and cannot get a passport or license of some sort (even fishing licenses can be withheld) doesn't mean there is a warrant out for that person. Many states now use a registry in the court system to track child support, and anyone diliquent is reported to the State Dept and cannot get a passport. Doesn't mean he's a criminal, just behind and one of the penalties is no passport/license renewals until it is cleared up.
I think he would be fine with a BC and ID. No agency is looking for him. A closed loop cruise will bring him back to where he started.
If there is a warrant out because he is so behind that it has been reduced to judgment and he has failed to appear when ordered to, I wouldn't risk it. Honestly, if he still has some visitation it is unlikely that there is a warrant out for him since the court would know exactly where to find him.
Just my opinion and NOT legal advice.