I have an early model Samsung WB and it still works brilliantly and it’s Schneider wide angle lens is great for shots where you can’t get back far enough. It has auto stabilise. I’ve also got a small Lumix TZ 80 which has LCD flat screen and also a viewfinder. It has high optical magnification so the viewfinder is useful to counter my “ essential tremor” in my right hand. Who called it an Essential Tremor beats me. No jokes about “Do you drink much?” please.Most of the newer digital cameras have auto stabilisation which helps a lot.
Another thought is to use a tripod or monopod to make the camera as steady as possible.
My favourite small camera is the Samsung the same as this one:
although I do have a Cannon DSLR for more studio work.
Shutter delay is a good way if the subject stays still. But trying to persuade wildlife to do that can be a challenge 🤭 I went to northern Spain looking for wolves and a friend lent me something akin to a rifle butt handle with an extension that you screwed the camera to. Never again. You can’t believe the hassle at Stanstead and Valallodid. But I did get some nice photos of wolves.Whatever camera you buy they will have a common tripod bush, so there are several steadying devices available. For convenience I have a 'Pod' which has an off centre tripod screw to suit may camera. I also have a 'gorilla pod' which has the screw and three flexible legs (about 6" long' that can be poised to fit various objects, but fits easily in a pocket. There are also some dedicated 'camera bean bags' or if someone is handy with a sewing machine it would be easy to make your own similar.
You could also look for a camera with a 10 sec delay - so you set up the camera with the shutter delay then you are not handling the camera as it 'fires'. Also a trad way to get yourself in the picture selfie style!
Enjoy your photography!