Cotton is very commonly processed to a very high purity, maybe 99% or so (ignoring water content) at least for textile applications.
I am sure this is somewhere available.
In the worst case couldn't you just buy white cotton fabric or yarn?
Anyways, it should be easy enough to attempt the traditional alkaline "scouring" process. However, I can see how maintaining an NaOH solution at near boiling for a few hours might be intimidating.
An enzymatic "bio-scour" process may work for you as well but it is no doubt intended for a very specific application that may not match your own. Specifically the normal problem is preparing the cotton to be suitable for dyeing. Any enzymatic process is inherently targeted at certain chemicals. In this case I doubt that it will be able to completely remove the pectin substrate.
If you think you really need purity I would initially go with the alkaline scour. If all you need is improved wettability then an enzymatic scour should be workable as well.
Or you could just go with silica
I'm always answering silica questions on these forums.
If it were me I would toy around with coating the cellulose with silica in the manner of TimberSIL.
Unless someone does that already...