Can you take a big tarp and one person on each side (so hopefully you are from a distance) pull it over the cage then the tarp will get sprayed and not you?
Not sure any other way as someone as to get close to the cage to open it...
As far as removing the smell, my Dane spooked a skunk last winter and got sprayed - I found this advice to be better than tomato juice although it did lighten some of the black hair on my Mantel Dane, but he is not a show dog so it didn't matter! You can hopefully apply this to you or whatever else got or gets sprayed!
Whatever you do, don't bring a freshly skunked pooch into the house! The dog will rub on things and tranfer the smell, then the whole house will smell like a skunk. If you must bring him in, wrap him in something washable until you get to the bathtub.
Skunk Smell Remover 1 quart 3% Hydrogen Peroxide
1/4 cup Baking Soda
2 tbsp Dish Detergent. The stuff for washing dishes in the sink, not something for dishwashers.
Mix the ingredients in a large bowl, because it will boil up like Vesuvius. We are, after all, making an oxygen generator. Wash the dog with this while it is still foaming, because it is the oxygen which reacts with the thiols in the skunk stink to neutralize the odor. If it sits around, it will loose it's efficacy because the oxygen boils off. Don't try to store it in an airtight container, because it will blow up. The brew also works for clothes, humans and unlucky cats.
Sometimes being chased by a dog is not enough to scare a polecat off the property, in which case, mothballs will do the trick.
Good Luck, I have been there!