Testing on my own computer, one workaround appears to be to use unmodified PrintScreen, leaving a hand free for the mouse, and quickly right-click for the context menu after the keypress but before the Save pop-up appears.
A PITA to be sure, but it does capture the context menu.
As for cropping down a full-screen capture, I tend to use PhotoFlare for jobs like that (find it in Software Manager) assuming you haven't anything else installed that does the job.