Pretty easy to do, actually. Well, not the randomly selected time, but at fixed times.
Create a new event. Set the Trigger to The clock ticks. Set the Conditions to:
secondsElapsed / 60 = 7
Add Actions that display a message about changing the game, one for each game. Press the Action Settings button and in the Messages section, select the behavior you want.
This would display one of the messages every 7 minutes during a round. Change the 7 to the time period you want (5, 7, 10, etc). It's probably best to make sure your round lengths are an even multiple of the time period you choose. So if you want to change hands every 7 minutes, your rounds should be 7 minutes long, or 14 minutes long, or 21 minutes long, etc. Now that I think of it, you might want to make sure the messages don't get displayed at the end of the round (when the clock hits 0, which, if your round length is a multiple of your hand change time, will mean a message would get displayed):
(secondsLeft > 0) and (secondsElapsed / 60 = 7)
You could also do this just by modifying the Rounds schedule. That might make more sense, actually. Make each round a change in hands. You could simply change the Game Name field for each round, but not increase the blinds except for every, say, 5 rounds (if you had 5 different games you want to play). The default layout already shows the Game Type and Game Name. Personally, I would probably go this route since the game information is always on screen and not just while an event message flashes on the screen.