I feel like you're missing something if you object to a treatment for alcoholism on the grounds that the treatment might cause liver damage. Alcoholism definitely will cause liver damage.
Naltrexone is generally safe for most, but in severe cases of cirrhosis it's not recommended. There are alternatives, but someone with that level of alcoholism usually needs to be clinically monitored.
If you're worried about liver damage please look into Acetaminophen.