Cardboard mulching on a slope, or should I?

We have two small areas of lawns in the front that I wanna get rid of. I dog up the left side myself and almost broke my back 🫠 came across this sub for some advice and everyone said just do cardboard sheet mulch.
But since I've already done the left side I'll probably just mulch the right, but there's a slope on the right and I don't want mulch to fly everywhere or slide down the slope

Need advice? What's the best way to "de-lawn" here?

Thanks.