Today's object is this boxy thing with a glass window and handle, indicating that it has a door.
At first glance it might give the impression of some sort of microwave or mini oven (even more so in other designs that can be found in the games) but with a brand name like that, blueish light and especially the scissors inside it's quite clear that it's not meant for cooking.
It is a UV sterilizer, a device that is used to decontaminate objects from microorganisms by killing them off with UV light or ultraviolet germicidal irradiation (UVGI) in a more techincal term.
With the scissors of a barber touching so many differnt people's hair it's only natural that they are put in such a device inbetween work to thoroughly clean them.
|A real UV sterilizer unit, much like the ones portraied in the game|
Devices with such a design are apparently somewhat popular with barbers in Asian regions so it makes perfect sense that the Shenmue games portray them how and where they would be seen.
Both barber shops in Shenmue have them and the same is mostly true for the ones on Three Blade Street in Shenmue II. The only exception is Zhangyu's place, wich fits with the rest of the rather shabby interior.
The brand name "Cleanstar" exists in real life. There are a bunch of different companies selling products or services under that name. However, none of them have a logo design like the one shown in Shenmue and none are offering any UV light stuff so there aren't any real life roots to it.