Well, if you go with the 2.25" measurement for the inside cube, that would leave you with 3/8" on either side. That would be if the walls fit together properly. Since they don't and the beveled edges need to be sanded smooth and to the correct angle, you'd likely lose a bit of space there. It would leave you with somewhere between 1/4" and 3/8". The wall thickness of the outer cube is 1/4". Take a look at the screen grab again, at the bottom edge. It's pretty close to a profile view of the wall and gap, and from the looks of it the gap is just a little bigger than the wall thickness.
As for the dark snake on white/white snake on clear, a laser engraver etches by melting the plastic, which mess with optical clarity, same as sanding would. So an etched design on clear appears frosted/white. If you engrave white plastic it has the same effect, it's going to end up white on white. Visible for sure, but not very well.
For me though it still all comes down to how horrible the prop would look with the snake that far off center. Even if they were on a tight schedule and if they had a low budget, if I was supervising and they handed me that I'd have chucked the inner cube right away and had them do it over. It's like $1 worth of acrylic.