Koetsu Rosewood - Best/safest way to clean stylus

I have a Koetsu Rosewood Signature and have been cleaning the stylus using LAST (I think that is the brand) liquid with a brush, followed by using the cueing to drop the needle onto a Magic Eraser 4-5 times. I think this works pretty well, but I worry about the liquid... having read about liquid wicking up the cantilever, etc.

Could using liquid damage the cartridge? Could dropping the cueing down onto the Magic Eraser "grab" the needle and damage the suspension as I raise it? It seems like the only safe way to use Magic Eraser because I don't trust my hands to be steady enough to do it any other way.

Is there another cleaning method that has actually been proven (via microscope) to clean the needle safely and be safe for the cartridge?

Thanks