I could be wrong, but I'm pretty sure that is not going to work for you.
In the first picture you posted you can see a remote reservoir/shock adjuster located above the shock. When the suspension compresses, the front pivot arm rotates so the arm is basically moved up, flat against the top of the track. Those white sliders push up against the track and the shock rotates so it's close to parallel to the pivot arm also.
That reservoir/adjuster is going to be pushed hard into the inside of the track.
Can the shock be rotated around and installed upside down? I'm not certain there is enough space for that either as the skid comes right up to the bump-stops hit the upper crosshaft on the pivot arm.
Can the reservoir be moved elsewhere?
Check it out before you ride it.