For years I used Arango Briar Pipe Wipe until, as far as I can tell, it went extinct.
When I could no longer find that, I switched to The Bee's Wax, a furniture/everything-but-the-kitchen-sink polish, that has worked fine on most of my briars. On maybe two of my pipes, this sucked off minor layers of stain which was disconcerting... but I still use it... worked into a clothed and then buffed off afterwards.
Finally, I found the below product... carnauba wax, olive oil, bees wax, and a few others. Excellent results on my pipes. The so-called light lavender scent, I've only noticed when using. It has left no remnant whatsoever, at least to my nose... which is pretty good, as well as large.
Both of the latter two products are available from Lehman's, somewhere in remote Ohio! (but you can order online also)