Lenses for Closeup Photos and Videos of hands cooking

I want to shoot photos and video of somebody's hands while they cook. I will be using a 5DM3 and can use either a 70-200mm or a 24-70mm. It would be nice to create some blur to the background and the video clips will be short clips and assembled into a short video with lots of quick shots.

I may not have enough room in the space to stand back far enough to use the 70-200, though if I can, would it be a good idea to zoom in to get my photos/videos or might I be better off with the 24-70mm and just get close up and zoom in? Just looking for any thoughts on this, since I am pretty new to it.

What is the better way to approach this?

Thanks.

A 70mm lens on FF at a distance of 60" will frame an area of 20" x 30"

A 200mm lens on FF at a distance of 60" will frame an area of 6" x 9"

A Canon 70-200 has a minimum focus distance of about 47.25"