Well, this has me vexed.
There is no "Shire Language" in Tolkien's work--The hobbits may have had their own tongue, and several words survive from it; 'Mathom', 'Smial', and so forth. But as of the Third Age and the founding of the Shire, they spoke "Westron" the common tongue. This is simply a fancy, in-universe way of saying "English". So the script for "Westron" is the Latin Alphabet--there is no record of a Hobbit or Shire Alphabet.
Next we can cross Dwarvish off our list. Their "Secret Tongue" was Khuzdul, for which the script was Runic Cirth. Runes are never rounded--they're made for ease of carving into stone and metal, so the characters are all made of straight lines.
Then we come down to Elvish. Note that the Dark Powers used their own tongue, but they did not use a native script. Any writing in the Black Speech was done in an Elvish mode. Tolkien devised three Elvish scripts that I am aware of--Sarati (the earliest), Valmaric (a bridge script between Sarati and Tengwar), and Tengwar, which is by far the most common and well known. If someone was actually going to engrave a pipe band in a Tolkien script, they would probably use Tengwar , or maybe runes.
This isn't Tengwar--or Sarati OR Valmaric. From there I checked it against various real-world scripts. Not Sanskrit, Pali, Devanagari, Arabic, Khmer, Greek, Phoenician. Not Chinese or Egyptian Heiroglyphic--they use ideograms. For that matter, not Demotic or Coptic Egyptian either. Not either of the two Japanese scripts.
Around this point I took a different tack. The pipemaker is a New-Zealander, maybe there's something there. But its not Maori. Not Tagalog. Laotian--now that's close. There are several similar characters--but still not a perfect fit.
At this point my eyes are melting out of my face, so I give up. My own assessment is that it doesn't say anything in any language or script--just a fancy band with random doodles. I hope someone with more knowledge can prove me wrong!
I love that shape, though. Never seen one quite like it.
-Josh