I need a small camera with optical zoom and full HD video capability for lefthand users. I saw some old samsung hmx camcorder, but there aren't new available. I think to use also a action cam, but are all with fix wide angle lens. The only solution I see is to use a small remote control (like gimbals) attached to the camera.
I am unaware of any "left-handed" digital cameras. However, some old film cameras, such as Exakta cameras, were produced with the shutter release on the left side. Also, Nikon considered, and produced prototypes of, left-handed F100s (per Ken Rockwell).
Manufacturers have little incentive to produce "left-handed" cameras because the vast majority of people have no difficulty operating the shutter button with their right hand, regardless of which hand they use to write with. I am fully aware that some people may be missing or unable to use an arm, but it is not up to me whether manufacturers produce such cameras. Several of the options I mention are applicable to such situations.
Use an unconventional grip. Some people operate two cameras simultaneously this way. Thumb on shutter button in right hand. Index finger on shutter button in left.
With Exif auto rotation, cameras do not have to be held "right" side up.
Operate the shutter button with the left hand, with the camera in portrait orientation. This works for cameras that have the shutter button set at an angle.
Attach a power grip with shutter button to the camera. Operate the shutter button on the power grip with the left hand, with the camera upside down. Caleb's answer has photos to demonstrate this technique.
Use symmetrically designed cameras, such as the Canon PowerShot N, which lacks a shutter "button". Most 360-degree cameras are also symmetrically designed.
Use cameras that can release the shutter in response to touch input, such as the Samsung HMX camera you reference.
Put the camera on a tripod or chest mount with an L-bracket to hold the camera upside down or sideways. Operate the camera with your left hand. This is the approach StessenJ used.
Write a letter to the CEO of your favorite camera company.
Learn to operate the camera with your right hand. Then you can use your left hand for other tasks, like writing notes or operating a computer. Similarly, right-handed people can learn to operate cameras with their left hands to free their right hand for other tasks.
Aside from physical limitations, which hand to use is a matter of motivation. I am able to perform many tasks, including writing, with both hands. Discomfort is transient, and dexterity comes with practice. Being "right-handed" or "left-handed" means you have given one hand decades of extra practice. There is little difficulty if you learn to perform new tasks with either hand. Consider that no reasonable person complains about having to use their non-dominant hand for tasks that require both hands to work equally well, such as typing or playing piano.
Some pictures of alternative grips:
How can I operate a modern camera when I must do so left-handed?
Add a battery grip and hold the camera upside down. This puts the shutter release and thumbwheel on the battery grip under your index finger, and also gives your thumb access to most of the other controls.
This works very well in portrait orientation with your left hand under the camera, since your palm can support the weight of the camera and free up your index finger and thumb to operate the controls. It's a bit more awkward in landscape orientation, with your bottom three fingers trying to hold the camera, but it does work. Adding a hand strap would help, and if you can support the camera on something (right arm, your knee, a monopod, etc.) there's no issue. (Shooting one-handed with your right hand is awkward for the same reason.)
Many smartphones work well left-handed. For example, the volume buttons on the left side of an iPhone work as shutter release buttons. It's easy to hold the phone in your left hand and trigger the shutter with your thumb.
I have some experience with operating a camera with one hand. Be it left or right, it is more difficult than with two hands.
I can recommend using a pistol grip. In the old times they came with a wire release operated by the trigger. For a digital camera you need an electrical remote control built into the grip. I don’t know if such a device exists in the market.
I was right-handed but then I had a stroke that paralysed my right arm, so that left me with little choice... I could press the shutter button on the HS-10 with my left middle finger from below, but the better solution was to put the camera(s) on a tripod. That leads to better photos and movies anyway.
And then, after a year and a half, when my hand slowly started working again, particularly the index finger on the shutter, I was so happy that I treated myself to a 6D. :-)
Not that I've ever done it, but you might be able to route a cable release to the left side of the camera to trip the shutter. I imagine if you have fabrication skills, you could make a left grip for most SLR type cameras (perhaps attached to the base plate and embed the cable release in the grip.