I was wondering if cutting the top off like in the picture is a must. Would it work without cutting the circle? Or would i need stronger magnets (those have a pull of 4.83lbs only) if i wanted to skip that step?
All depends on the height of the box. No need to cut a hole if the setup can spin underneath the box lid and not be too far from the stir bar in the flask. The magnets in the OP are beefy. Not cutting a hole if the box allows should be a non-issue.
My assaulted cigar-box is as ugly as they come. Hole for necessity. YMMV