In the military, a combination cover (aka hat) can be disassembled. Take the cloth cover off and wash it...maybe by hand if you're not sure how sturdy it is.

The leather band can be wiped clean or replaced once the hat is disassembled.

If the hat is so cheap that it can't be taken apart, probably best to throw it away. You could try putting it in the washer first, maybe it will survive.