I can hardly image that there are keyboards without, they usually have it in a combination with a “Fn” key. I believe that it used to be F12 or Fn + F12, but maybe they removed it.
But even if there isn’t, you can change the hotkeys in Greenshot
Just go into the preferences, and there you can specify which key triggers which functionality. Just click into the field, and do your hotkey combination. If you press OK it’s stored.
There might be some key combinations which do not work, especially the “Windows” key… but try and you will find a solution.
Yes, it’s unbelievable. But there is no PRINT-KEY. And the F12-KEY ist is occupied from a unknown app. FN + F12 is blocked for FAVORITES. There is also a Favorit symbol on the key. If You want, I will send you a picture of the keyboard layout.
Now I followed Your hints and it works! I have used F1.