I got non-skid stair treads for myself, after falling down my stairs. My dog still can't go up the stairs! He's a sled dog breed, can run up a very steep cliff face in a flash, but can't handle a wooden staircase with two turns. I think it's the turns that defeat him, maybe?

I've got the adhesive kind on Amazon. They claim it does not damage the finish. Honestly, I don't care - it's a better deal than than broken bones.

We have 2 dogs and they do well with these bullnose stair treads. They come with double-faced tape but we used small carpet nails to hold them in place.

https://oakvalleydesigns.com/

Also looking for a solution that won't ruin stair finish

We just refinished a small stair way in our house, 7 stairs. But our dog is having issues with no carpet. Any removable non skid treads that work. We don't want anything with adhesive.