After use dampen a cloth with denatured alcohol.. very little water content, and wipe down the ferrule and shaft. Then burnish with leather. No damage due to water. No loss of wood due to abrasives.
Magic Eraser is the best for ground in dirt but it leaves the shaft in need of a little sanding... not much but just a little. No need to use this on a new shaft but if your shaft is dirty now just dampen the Magic Eraser with alcohol and clean the shaft. You'll be amazed! Then sand very lightly with 600 grit and again with 1000 or 1500 and then burnish w/leather. I'm not an expert but I think an expert will tell you the same.
Just clean w/the alcohol and burnish w/leather after every use!
Congratulations on the quality cue acquisition.