Remember with kinks: consent should include anyone involved in your scenario, even people just walking by! I'm not gonna say you can't be risque in public, but definitely be careful. There are ways to do what you describe ethically but make sure you minimize the risk of subjecting others to a kink they did not consent to.
Going out bottomless in a skirt seems harmless enough assuming the skirt is long enough to fully cover your bits plus some.
Going into a forest and stripping down can be risky, not to say you can't do it but try and make sure you're well off the beaten path and do your best to make sure random people don't actually stumble upon you. They're just trying to enjoy their hike/walk more likely than not, and running into a naked person in the woods doesn't exactly help.
It's a tricky balance especially when the thrill is in the possibility of being seen/caught, but it's important to be able to separate the fantasy of the situation from the reality. People just going about their day shouldn't have to deal with the surprise of running into someone expressing their kinks in a public space.
Depending on where you live, be careful in outdoor areas with tall grass because there could be ticks! Of course you could get ticks even clothed but if you're stripped down you're practically inviting them into the crevices they prefer. I'm unfortunately speaking from experience here (luckily they weren't a species that feeds on people but eww I'll never fully forget that crawling feeling all over and not knowing if I got the last one off 😰).
When I go to a nudist or naturalist resort, I take it off, as honestly, IMHO, showing people your cage in a non-sexualized arena like a nude beach is not cool.
However, I've gone to sexualised nude hot springs, and other areas where I have worn it. I've also done quite a number of scenes where I as the sub never got let out of my cage at all, and got tied up and beaten nude with cage on in front of hundreds of people.
All that said, I'm also not an exhibitionist so to me it was just natural to be wearing it, as I always wear it. It's just a part of who I am.
As someone who's into both exhibitionism and chastity, but agrees with the idea to not incorporate non-consenting people in one's kinks, I've thought about kinky sex clubs. I'd love to be in there wearing a chastity cage. I don't have any experience to share (yet :)