There's a good book from a former Smithsonian curator called One Good turn that talks about the ancient history of the screwdriver and the screw.
If you went back in time far enough that the people around you didn't know about the screwdriver and the screw, Even a rudimentary knowledge of It's existence would possibly on its own break the timeline.
Or just sketch what you want and have a metalworker of the period make it. They would have had the precision to manage it particularly if you sacrificed quality and worked in pewter. Pewter is so easy to cast you can pretty much diy.
The Phillips head screwdriver screws are great for not exactly needing the most precise shape for undoing them. Anything sort of in the ball park will work.