Stage one step at a time
Before opening a device or fixture, clear a rectangle of bench space. Place the removed parts in a tray in the order they come out. If there are different screw lengths, use separate labeled sections or draw a rough map on paper.
Know what a magnet misses
A magnetic wristband can hold some compatible metal fasteners and bits nearby. It will not capture every material, and it cannot tell you which screw came from which hole. Keep nonmagnetic pieces and tiny washers in the tray.
Reset before the next step
At each pause, count the parts you removed and check the tray. Close containers before moving the bench. Empty any magnetic holder rather than storing it with mystery fasteners attached.