top tip: use an ice cube tray to hold all the screws you remove. I remove the first set, put them together in the first cube hole and continue. then just reverse the order of cubes when you are putting it back together.
I've been bitten by that scheme after I'd carefully disassembled my laptop, putting all the screws on a neatly labelled sheet of paper, only to later attempt to blow out some dust, and have them scatter across the desk and floor.
Double-sided tape, or actual compartments, sound like a much better idea.
Another strategy is to screw them back in, lightly, into the same holes they came out of (after removing the thing they were holding down of course). Not practical with a lot of gear though.
And use wide masking tape over each cube as you are done so that when you (or the cat or the kids) knock it the screws don't disappear into invisible cracks in the floor.
Actually I tend to have strips of tape attached to my desk, with the sticky-parts up. The ends are turned over and stuck to the desk.
I stick the screw heads to the tape. They stay pretty well, are easy to get-to, and it's easy to arrange them as you want. I usually put them in a compacted form of the layout they were on the board.
I just put the screws back into the screw holes that they came out of, after removing the component that it was holding in place. And take lots of pictures along the way.