I don't really worry about the chalk dust in the shaft, I clean my cue after each use and it will build up a blueing over time. That doesn't mean my shaft is dirty its still smooth as brand new. What I don't like is putting all kinds of crazy chemicals on the shaft wood, or sanding it to clean it.
It takes a long time to break in a shaft right, and sanding will ruin the dimensions eventually.
Rossingol lighter fluid works just fine on a cloth, I prefer it for cleaning than anything else as its oil not water and can't damage the shaft or cause it to warp...if anything it will seal it better. Plus petroleum distallates are usually good for getting gunk out of just about anything.
Once you got your shaft like you want it, then just always keep your hands clean. Then clean your shaft after each or during each session if you play long enough.
Take a damp papertowel and buff the shaft hot, then take a dry one and buff it hot again, finish it off by buffing with a piece of brown cardboard....good to go perfect every time. You do that and you wont wear out the dimensions you like, it wont ever get sticky or dull, and should stay clean tho after some years the shaft will get darker but it will be more even in color not splotted with chalk.
Thats the old school way of doing it, people talk about all kinds of products but this way is the tried and true for generations....and you don't have to buy nothing just a paper towel and some old cardboard.
The only time I ever need to put one of my shafts back on a lathe to be "re-conditioned" is if i damage it and put a dent on it or scratch the heck out of it. New clean shafts get dingy, sticky and unsmooth b/c of dirty hands, especially wet/oily dirty hands. The damp cloth +heat/friction break down all the old skin oils and goop, the second dry cloth gets the excess and cardboard burnishes baby smooth.
It works alot like trying to get cigarette smoke off your winshield, alcohol and newspaper....the alcohol + the friction of the newspaper is what takes it off....better than windex and all the other crap.
And remember just a DAMP CLOTH, NOT WET!!! Once you stark wicking the shaft with the damp cloth up and down really fast it shouldn't be but maybe 10sec or so till its basically dry. If its damp the pores wont really open up and your going to just remove the surface residue (exactly what you want) if you use a wet cloth/papertowel then its going to open up the pores and it'll be harder to get that perfect sealed/smooth burnish with the cardboard.
1)buff w/damp paper towel
2)buff w/dry paper towel
3)burnish/buff w/ brown cardboard
anything else is just uncivilized IMOP lol