Aaaah yeah! Just use a micro controller. If you program in C there should be a function like rand() that will generate a random number for you so that you can randomly get 1 to 10 as a delay. You probably wouldn't have asked this question if you knew about micro controllers. Anyway that's how I would do it.
When one person suffers from a delusion it is called insanity. When many people suffer from a delusion it is called religion.
I doubt you'll find a circuit that will do almost exactly what you want. Everything is computerised these days compared to a few decades ago. You should learn how to make use of microcontrollers. I never had help from anyone, I taught myself. You can get premade microcontroller boards from the SparkFun website. They sell nice stuff there. Just get one of them boards and hook up whatever devices you want to it. You program the microcontroller in whatever language and mission complete! You'll be proud of yourself. I kick arse in microcontroller class.
When one person suffers from a delusion it is called insanity. When many people suffer from a delusion it is called religion.