I have a Sony DSC-W800 camera, and I want to know if it is possible to get a remote shutter release for it.
No. This is a budget compact camera made for portability and convenience, not for advanced functionality. There are no accessory ports and no wifi or bluetooth control.
Well, there are old-style pneumatic/mechanical cable releases that can be physically strapped to a P&S camera, to press the button remotely. But you are limited by the length of the cable.
Wireless remotes do not exist, because the camera itself has no wireless receiver capability or ports to access shutter function.