OK, not a clip or strap, but I have a new favorite small camera to recommend: The Canon M3 Mirrorless. Compact, reasonably light (about 1.25 lb with kit lens) and packs a lot of power with its 24MP APS-C sensor. With its smaller scale (which it gains largely by relying on its LCD screen and giving up its prism/mirror system), it uses smaller, lighter lenses. It also has a lot of customization, which some of the earlier Canon compacts lacked (e.g., customizable picture styles that allow you to get those good, high-contrast/saturation Fuji Velvia-style landscapes). On a recent trip to Maine, I shot pics that also drew a lot of praise and stood up to high-quality 16X24" enlargements. I've been most pleased!
The low weight also allows me to take a smaller tripod that I can easily slide in an old stuff bag and slip in my pack.
The downsides are relatively slow focusing and back-panel buttons that are too easy to hit and re-set some of your camera settings. The smaller lenses are not a crisp as big lenses, but the quality difference seems to be small. For me, these are not show-stoppers--worth it for the +++ I otherwise get. It means a lot to me to have a light camera on either a high-endurance hike or when going into a new area that I don't know will yield great views.
I always hike/climb with my camera looped over my neck and one arm. I accept the risk of a busted lens or filter as part of the tradeoff of having my camera ready to shoot. (And if the shot is good enough, I stop and go for my tripod.) Yes, I have fallen and once smashed a good polarizer in Big Bend, but the camera and lens both survived OK. (This is one of many reasons you should ALWAYS keep a filter on any lens worth having.) I carry spare lenses in a waist pack in Zing pouches and always carry a spare dry bag in case of serious rain.
OK, thanks for letting me ramble on. If any of you have or get one of these (or another light mirrorless), I'd enjoy hearing about your experience.https://www.bhphotovideo.com/c/product/1180767-REG/canon_9694b011_eos_m3_mirrorless_digital.html