I have always seen manipulation at this scale done via micromanipulators (wire bonder or inside of a vacuum chamber)

When you need precision movement, the alternative to micromanipulation is using a XY stage like ASML uses.

XY let's you hold an object like a wafer or part, and move it around in certain planes while not moving in others. XY and even XYZ stages are not uncommon in vacuum chambers where parts need moved but repeatability is key.