For older versions, use SnagIt's capture delay timer. When using the delay timer, after hitting the hotkeys the capture will not occur for a pre-defined time period, giving you time to manually open the dropdown or menu.
Select Tools > Timer Setup > Delay / Schedule. Check Enable Delayed/Scheduled Capture, and select Delayed Capture. Then set a short delay.
Press the hotkeys to begin the capture, and then open the dropdown menu as the timer counts down. When the timer reaches zero the screen will freeze and capture will occur.