I would just cover it with some exterior wood paneling or board and batten (style of exterior wood paneling) and paint or stain it.

Are these the rigid shingles, that are cement based?

If so, trying to nail anything over them will be an exercise in futility. Whether it is wood paneling or any kind of lath for stucco. The shingles came from the factory with holes for nailing.

If you try to drill thru them for nails, you will be creating a lot of dust, much more dust than removing them would.

And you have to consider how adding another layer of siding over the shingles will impact on the cased openings and trim. Will the new layer stand proud of the existing trim around doors & windows?

In some areas, homeowners are allowed to remove them themselves. Have you checked into the rules in your area?

I agree on checking to see if homeowners are allowed to remove them in your area. We are in this area. You could use the lead paint guidelines with good results to contain any dust you might create.

it is a hard cement based shingle. I have very little home remodeling experience and I don't want to put my family at risk if I do it wrong so I was hoping to cover it in stucco or someone similar. I was hopping someone would know what was best and weather it would stay in the wall and not fall off.

Potentially vinyl siding but I would think stucco would be a big no.

Paint it. It sounds like you really don’t want to do anything that will disturb it and putting a material over it will disturb some of it because you’ll need to drill through. Paint won’t disturb it.