How can my husband get custody of my child in the case that I died.

My son is almost 6 and has never seen him or paid any child support to me. My husband has been in his life since he was 3 and our son only knows his as his father. He pays for school tuition, our son goes to private school. He has financially paid for more than half of his living expenses the last 3 years. My question is in the case that i died when he be able to get custody of our son. Would i be able to get paperwork drawn up stating that he would be his guardian considering his biological father has never been in the picture and is not on the birth certificate. We have considered adoption and my husband would love to adopt him but our son has alot of medical expenses as he is ADHD, Has severe asthma and immune system issues. I get medicaid at the moment and if he were to adopt him we wouldn't qualify for that and it would be a huge financial task for us. So is there anything i can do to put my mind at ease. His biological father has no legal rights currently but I'm afraid if something were to happen to me he would try to get him just out of spite and for death benefits that our son would get. Thanks, Lindy