Carpet Cleaner Steamer

Hand held steamer on area rugs?
I have two area rugs that need cleaned. They aren’t stained, just a bit dingy looking from my lab laying on them. One is a jute type rug, 8×10, and the other is a mixed type blend 7×9, it does have some wool in it. I was just wondering if I could use my hand held steamer, I have a Shark Steamer, to clean these? Will it hurt them?
If I do this, what should I use with it, just water or some kind of carpet cleaner, etc?
The steamer I have is not one that sucks the water back up, I was thinking of hanging the rugs over my deck rail and cleaning them, that way the water can run off as I do it.
It is not a bunch of money to have them cleaned by professionals.
It is cheaper if you take them to the cleaning company and pick up.
I highly recommend Serve Pro, if they are in your locale.
When they know what the soil or stains are, they’re very successful. Pets leave oil from their fur and skin.
I am not associated with them. I’ve used them when I owned my own floor covering business, 35 years, Ret.
Jute can be tricky. The mixed fiber rug may have polypropylene and should not be cleaned at a high temperature.