As long as you get there early and don't dawdle, why wouldn't it be able to be done?
The park opens by 9:00, if you get there by 8:30 to be early in line, and go straight to the safari, you'll be done by 9:30ish. It doesn't take an hour to get to the other side of the park unless you're walking really slowly.
You don't need a shortcut, it's really a no-brainer.
Anne