He doesn't appear to want [to cause] any trouble.
He appears not to want to cause trouble.

I think my choice would depend on the context.

He doesn't seem to want to cause any trouble.

"He appears not to want to cause any trouble" is also possible, but it's not the way I'd say it.

The context is that someone is involved in an argument between two groups of people, but he does not seem to want to fight because he does not want any trouble.

Is the gerund wrong here?

Yes, the gerund is definitely wrong.

I'm still not sure which version I would pick, but in reality I don't think it matters too much anyway.

OK, thank you. I think I'll use "He doesn't appear to want any trouble."