I've been keeping my chams outside all summer since the mid 90s.
I use reptariums, but have also used home-made wire screen cages in the past.
I had a raccoon once tear into a wire-screen cage and eat a whole clutch of dilepis babies that were several weeks old. He left a poopie in the cage which I took to the extension service to identify what sort of animal it was. This was the only problem with a wild animal I've had, and it was near the beginning of my outdoor housing experience and it was a large screen cage that sat directly on the ground. I moved my cages onto tables with short legs maybe 20" or so off the ground and I've never had another animal related problem, in spite of living in the country and seeing all kinds of wildlife and stray cats and dogs walking along between or near my rows of cages- stray dogs and cats, oppossums, skunks- even a bobcat one time, and coyotes too.
The other problems I did have with lizards were fireflies killing my bearded dragons at first (solved with reptarium zipper doors) and a Dennis the menace type 5 year old who let my colony of corucia loose after driving his little battery powered 4WD vehicle all over my neighbor's beautiful vegetable garden and flattening it for the summer (solved by his moving away).
Not too bad for years and years of beneficial fresh air, real sunshine, lower power bills, and green-keeping of my lizards... I highly recommend thinking it through carefully and giving it a try on a weekend or something when you will be home to monitor the situation at first.
I provide constant shade and sun, and during the heat of the day when temps are up in the 80s and 90s I provide a fine mist in part of each cage (so the lizard can choose to be wet or dry, shade or sunny).