I think what you're wanting to do is add the touch behavior and the buttons. Then, take each of your commands, make it an "or" block, then add in the new condition. For example:
Keyboard: Down arrow is down => Player: Set direction to "Down"
Keyboard: Down arrow is down
Touch: Is touching DownArrowObject => Player: Set direction to "Down"
You keep all your old events: you just have to add conditions to them. As an added bonus, I think putting in touch controls like this automatically puts in mouse controls. I THINK.