Keep in mind that alcohol will probably adversely affect the finish if the rim is painted, shellacked, or varnished. Alcohol can also dilute the stain, especially if used often and/or aggressively.
That said, I use alcohol occasionally (most of my pipes are just stained), and more often on plateaus because they're a real PITA to clean; I follow it up with a little mineral oil on a clean rag.
Some puffers use wax, I don't. Commercial pipe buffing clothes by Dunhill and others are available, work well and these cloths last a relatively long time when used as the final touch to cleaning the wood.