Installing an acrylic glass pane as a one-sided shower cabinet - feasibility & tools

I'm moving into a new place at the end of month. It's in the attic of a tenement building, and all the wall (and ceilings) are drywall.

My first project is the bathroom: The bathtub doubles as a shower. Since it is a bit squeezed in between the slope roof and the sink, no shower cabinet has been installed. The former tenants installed a triangular curtain and supposedly showered while squatting down. See the picture for more details.

I am planning to both install a shower head on the ceiling (this is another question) and a one-sided shower cabinet in order to prevent the area around the sink from getting drenched every time I take a shower.

The bathtub is 75 cm (2'6") wide and there's 187.5 cm (6'3") space between tub and ceiling. The sink exactly does not clip the space above the tub, so I could install a cabinet directly at the edge of the tub. See the following image (I apologize for the rather crude drawing):

While I would prefer installing a pre-constructed cabinet made from glass, two issues prevent this:
There is a recess between the bathtub/sink/toilet and the actual drywall, which likely houses the drainage etc. This recess is about 120 cm (4') high from the ground (only 66 cm (2'2") above the tub) and 29 cm (almost 1') deep. Installing a heavy glass pane relying only on these 66 cm for support could be rather unsafe. Also, the recess would reduce the effectiveness of any single-pane cabin. As already mentioned, the walls are all drywall - I'd rather not try to mount anything heavy on them - thus, no glass pane, again.
Therefore, I am planning on using acrylic glass (most likely 5 mm thick), which would allow me to make the cuts which are necessary in order to fit the recess. U-shaped plastic profiles would be glued to the tiles and the edge of the tub, in order to keep the pane roughly in place, then I'd secure the pane all around using silicone. Most likely the pane will not reach all the way to the ceiling and thus have to be fixated using a retainer (which is available for purchase at my local hardware store).

Actually, this leads me to two connected questions (I have never worked with acrylic glass before): How do I best cut the pane (tools & what to watch out for during the process) - and would it even be sturdy enough to not to wobble all the time?

ps: If the whole idea is nuts and/or I overlooked some mayor detail, please tell me so.
#Bathroom #Bathroom-fixtures
Bathroom Bathroom