Yes, you can throw in shredded paper in the compost pile!
Just make sure you have your pile fenced in because it will blow around with the wind.
A few things to keep in mind: don't use colored and glossy paper, which might contain some toxic heavy metals. Newsprint and other paper is safe to use as mulch or in compost. In fact, one study revealed that paper had less toxic material than straw or grass!
It's best to mix the paper in thoroughly with the compost as you are doing. Just make sure you don't have a mass of paper together when you get it wet. It becomes impermeable.
The only problem with paper is that if you put too much of it in your heap, you could get an unfavorable carbon-to-nitrogen ratio, since paper is high in carbon.
You can also use shredded paper with worms.
The producer of this video can be found at OrganicGarden123 on Youtube and he welcomes your thoughts about shredding compost!