Sending Keystrokes to a Window when it Loses Focus
A way to trigger it with a global keyboard shortcut (and without having to switch back) is to create a little applescript to do it for you.  I'm not familiar with Virtualbox's windows, so you'll need to modify the below to suit your needs.  You can run it as is, and note that 1) Terminal does NOT take focus when you run this, it stays in the background and 2) when you do switch to terminal, the Inspector will be showing.

tell application "System Events"
  tell process "Terminal"
  click menu item "Show Inspector" of menu "Shell" of menu bar 1
  end tell
end tell


I'm assuming that the Pause VM command will be available from the VB menus, if not, please let me know in the comments where the command lives, and I can update the answer to reflect that.

Once you have the applescript tested, use Automator to create a service: this will let you activate it with a global keyboard shortcut, no need to switch applications or anything.


Launch Automator
New project if it loads an old one, and select "Service"
In the search box enter, "script" to filter the options and double-click "Run Applescript"
Paste the applescript right in there.
Save it, give it a name like "Pause the dang VM", and quit.


Next, to give it a global keyboard shortcut:


Open System Preferences -> Keyboard -> Shortcuts Tab
Select "Services" in the left pane
Scroll to the bottom of the right pane, and you should see your new service
Click "none" to the right of your new service and you can create a shortcut.


So now if you forget, at least it's just a key press instead of a whole application switch around. 

NOTE: you'll need to allow Automator to control the computer in System Preferences -> Security &amp; Privacy -> Privacy -> Accessibility