Is there a risk of mixing DEET with pesticides containing Permetherin?

Permethrin is a suspected human carcinogen.

DEET is an acetylcholinesterase inhibitor. It's considered safe enough to use on human skin (in low concentrations).

A mixture of a permethrin-based insecticide and a DEET based one shouldn't be any worse than the permethrin one alone.

We'd have to know more about what kind of risk you're talking about to give you a better answer than that.