sanding clear perspex never gives a uniform translucency, the scratches always show. the process that would be equivalent to etching it is to apply a solvent, ideally you would use ether as a solvent but it is very hard to get hold of nowadays, cellulose thinners works, but again it is not particularly good for creating a translucent effect.
perspex is a trade name for polymethyl methacrylate (pmma) made by ICI. the same material is also called Oroglas when made by Rohm & Haas. both companies make thousands of hues and transparencies - the trouble is actually buying some if you want less than a truckload.
I use a company called brighton plastics, who are based in brighton strangely enough, they will sell a sq metre, but dont stock all translucencies. (translucent being the effect that you want rather than transparent). a web search for pmma, perspex, oroglas or poly methyl methacrylate should find you a supplier nearby - perhaps mail order.
If you really cant source some pmma I would suggest:
1 try sandblasting - this is the only way to remove the transparency evenly but will never make the clear stuff any more misted than tracing paper.
2 buy some self adhesive window frosting from a local sign company (one of those places that does sticky plastic lettering - they will sell it by the yard) and stick it to the back of the perspex, so the front stays shiny and grease wont show if someone touches it.
3 consider putting something else under the clear plastic that has the desired translucency - like nylon, paper or cloth.
4 if you are using it for backlighting you may find that white perspex is the best thing to completely diffuse a light source - you can often make this even better by lining the 'lightbox' with tin foil.
a few tips for using it when you get it - perspex work hardens when you cut it, the result of this is for tension to be set up internally and thousands of small cracks will appear in time. to avoid this always cut it at a slow speed using fine toothed metal working saws - if you cut too fast it will melt and sometimes weld itself back together behind the blade.
likewise drill it slowly with a sharp twist drill, the same you'd use for steel. as for adhesives the cleanest way to weld perspex is to use ether squirted into the joint with a syringe, alternatively you can use a perspex adhesive (such as tensol) but these are always a bit syrupy and very hard to avoid getting where you dont want them. adhesives will show up the work hardening.
you can always polish out edges of cuts, scratches and smears using finer grades of abrasive paper following up with a buffing wheel.
