You can activate Void Stalker’s ability targeting a creature you control, including Void Stalker itself. In that case, only you will shuffle your library.

If Void Stalker leaves the battlefield before its ability resolves, the target creature will be shuffled into its owner’s library but Void Stalker will remain wherever it is.

If the target creature is an illegal target when the ability tries to resolve, it won’t resolve and none of its effects will happen. No creature will leave the battlefield and no library will be shuffled.