I use Keyboard Maestro to do just this.
I mapped the F16 thru F19 keys in this order.
F16 Left monitor move left
F17 Left monitor move right
F18 Right monitor move left
F19 Right monitor move right
I created 4 Keyboard Maestro Actions for this, one for each monitor and one for each direction. Here is the basic shortcut which gets adjusted accordingly:
Move the mouse over to whichever monitor without clicking.
Keystroke Ctrl-[left arrow] or [right arrow], depending.
Actually I changed the Keyboard Shortcut in System Preferences under mission control from:
Ctrl-Arrow to move left/right a space to:
Shift-Control-Option-Command left/right arrow to free up the simpler control arrows for other activities. I also changed the Keyboard Maestro Macro to reflect the change.
While at it I also have the following mission control operations.
F13 Show desktop
F14 Show application windows
F15 Mission Control
I have it set up for the mouse to stay on the changed monitor but it could easily be set to return to where it started from.