For filament, the best you can do is probably translucent, even if you go perimeters only (no infill), you're going to see lines at the seams between layers and together, they will make it look a little hazy even with completely clear filament (actually, standard prints of a couple mm thick work pretty well as diffusers, especially if they have some raised geometry for texture.)
Resin printers can do a better job, and especially for thinner walls and flat sides would probably do a nice job. With the right AA and small enough pixels, you can get pretty good results on curves or lines that don't match up with the LCD's grid too, but there will be that surface microtexture from the edges of pixels. An option here could be printing and then lapping the sides, but this isn't so easy on internal edges.
As someone else mentioned - laser cut acrylic may be perfect. It will be the most clear and should be able to handle flat sided geometry really well. Using an acrylic welding glue and some clamps/forms/jigs (probably nothing special), you should be able to assemble precut pieces and have next to no visible marks at the seams, plus better clarity of the plastic itself.