Magic Eraser is pretty much the standard in shaft maintenance.
Many repair men use it. Alcohol evaporates quicker than water so it is preferable in that you don't want to raise the wood grain of the shaft.
Something else you might like to use is ammonia. I got a large jug of the lemon scented for a little over a dollar. It can be hard on the lungs so if you were to use it, I would suggest using a respirator.
If you are planning on using a finer grit sand paper, keep in mind that you will be baring the wood. I would strongly recommend the use of a sanding sealer before you wax and burnish the shaft.
Chris Hightower sells a Shaft Sealer that I use. Its works great and I apply cue wax over top. other than that, there are many wood sealers that will work as well.
Regular shaft maintenance is something that anyone can do at home with a minimum of supplies and tools.
There some cue supplies out there that are just regular cleaning products
repackaged for the Billiard industry.
You know the expensive little bottles of cream cleaner with grit in it?
Try using Vim. Still, in saying that, be careful in reading the label on anything that you are planning on using. Some cleaners may contain ingredients that you might not want to put on your shaft.
Another product is Q Silk. All that is, is a ladies hair care product for the frizzies. I bought a bottle of Pantene only because it was on sale for $9. Lifetime supply right there. You can put some of the Pantene into a smaller bottle that will fit in your cue case.
The spelling might be wrong but look for any hair care product for the frizzies that contains dimethycol.