Chemical cleaners including acid based clog discovers up to 10% strength are okay. See their website here
You wouldn't want to leave it in your tank too long so best to head to a dump station straight away.
I wouldn't use a drain cleaner though. I'd use a wet vac to empty the sink and drain and then remove the trap and clean it by hand. I don't mind dealing with yuck though so...
If you're worried about harsh chemicals on the rest of the system, if the tank is nearly full when you start and you can dump it right away it won't be a problem, but you could go with the slow but steady method using an enzyme based cleaner. It will take a while but it will do the job.