Leo,
I don't recognize the format of the histogram you posted. Here is the histogram I obtained by opening your posted original in Photoshop:
https://photos.smugmug.com/photos/i-.../i-G5bgjXX.jpg
I was making only two points. First, your camera should be capable of clean images at least two, probably 3 stops above base ISO without noise reduction, provided that you don't have to boost shadows much (and possibly even if you do). Second, in the case of an image that doesn't span the entire dynamic range of the sensor--like this image--you can minimize the effects of using a higher ISO by exposing to the right.
You added another issue: are you better off raising ISO and exposing to the right or exposing less and amplifying the image in software? The answer to that depends on the camera. If I understand correctly, in the case of cameras that are misleadingly labeled "ISO-less", the answer is that it doesn't matter. In the case of other cameras, including mine, you are better off raising ISO and exposing to the right, at least at relatively low ISOs. I believe this is a function in part of where in the electronics the amplification is done, but perhaps someone who knows more than I about this can clarify.