These cardboard mailers are the ones I use to try to avoid the higher costs for shipping. Sometimes it works. Every now and then I get some hardass at the post office who says it isn't flat enough and sends it through postage due, one was returned (I was mailing cloth masks in them.) A CD should go just fine.

You can mail it like a first class letter and keep it low. A first class large flat envelope is $1 for the first ounce and each additional ounce is .20 cents. Up to 12 ounces, I think? But you're looking at 1 or 2 ounces tops for one CD. You'll probably have to write "first class letter" on it to be clear your intentions.