No, you don’t need to disassemble the laptop.
Laser engraving is performed directly on the surface of the keys, without any interference inside the device.
The technician carefully places the laptop on the laser’s work surface, focuses the equipment at the key level, and applies the engraving with high precision.

The process is completely safe — neither the keyboard nor the electronics are exposed to heat or pressure, as the laser only affects the top layer of plastic.