Ok, skunks and weasels are two different things. You'll *probably* be ok with what you're proposing.
Be aware that you are putting your chickens at risk by leaving their coop open at night if you don't have a covered run and well protected perimeter around your run (protected against digging with an apron, etc.,.). Also, for overnight defense the run needs to be made of the same hardware cloth normally used to secure coops which would be 1/2" wire or smaller. It is much easier to let the chickens have easy access to the run rather than opening and closing the pop door each day, but it is also much harder to secure an entire run than it is to secure a coop.
Best wishes,
Ed