Here's an approach: When you hear Skype ring, run a script that acts as follows: (1) Get Skype pid number, (2) Get list of all windows, along with process pids, (3) Using pid (or possibly window name) find appropriate window id, (4) bring that window to current screen and raise it.
For (1), you could use the usual
ps ... | grep ... approach. It isn't clear to me what sort of window or box the "answer button" is in; it may be that using a window title (instead of a pid) to find the relevant window in
wmctrl -l output might work better. For (2),
wmctrl -lp. For (4),
wmctrl -R ...
On this system I don't have Skype or multiple monitors, so cannot test above suggestions. I think a more-streamlined method can be worked out.
In creating and testing such a script, it might be a good idea to create a stand-in process that you can park off-screen and try using
wmctrl manually to bring it on-screen, before trying to script the process.
Regarding the "When you hear Skype ring, run a script" portion of the answer above: If you want to make a menu button such that the script runs when you move the mouse cursor across the button, examples of doing so using yume3 are found in
yume-wmctrl-leftcol which are in yume3-22.gz at yume3's download page. yume3 is Gtk-based, and easy to install if your system has Gtk libraries already installed on it. yume3 has option settings to make menus sticky / on-top / undecorated, as explained here.