I haven't tested it, but try something like this:
#!/bin/bash
qvm-copy-to-vm $(zenity --entry --title='Send to VM' --text='Destination VM') "${BASH_ARGV[@]}"
Save that as an executable script, such as "~/.local/bin/send-to-vm.sh". Then, open dom0 file manager, right click any png, click open with other application, and under "use a custom command" enter "send-to-vm.sh %s". Then, when you take a screenshot, instead of choosing "save", choose "open with..." and see if your script shows up in the list of available applications. If not, you might have to write a simple .desktop file in ~/.local/share/applications in order for it to show up as an option.
Again, this is just an idea off the top of my head and totally untested.
Okay, no offense, but that's pretty much *exactly* what I described. The idea is that from the screenshot menu, instead of clicking save, you click "open with send-to-vm.sh", and then a zenity GUI window will pop up asking you for the destination VM name. If you want a list to select from, change it to something like `qvm-ls | cut zenity --list`. I don't see how it could be any more integrated. If you believe I am mistaken, please point out exactly how my solution differs from what you're trying to achieve.
You might also be interested in the Qubes Screenshot Tool instead
https://github.com/evadogstar/qvm-screenshot-tool
> I guess the PrintScreen "app" is a simple script,
> hidden somewhere, as well? I'd like to extend it. Bernhard
No, it's a binary. https://git.xfce.org/apps/xfce4-screenshooter
The PrintScreen key is mapped to screenshooter by default, but you can map it to something else via System Tools > Keyboard. You can also remap it to "screenshooter --open send-to-vm.sh" to skip the save/open/upload dialog and instead go right to the destination VM dialog.
See also
https://docs.xfce.org/apps/screenshooter/usage
https://askubuntu.com/questions/252738/configure-xfce4-screenshooter-settings
https://www.commandlinux.com/man-page/man1/xfce4-screenshooter.1.html