I can't think of one, but it seems likely that there's been at least one such Hobbit, possibly being a bit like Don Quixote of La Mancha.
What about the original Took that invented golf?
Bandobras Took? Yes, I thought of ol' Bullroarer, but I'm not sure whether he was a warrior by preference or if circumstances just forced him into the role. Those Hobbits who took the role of Bounders to protect the borders of the Shire might be some good candidates. We can also look to the Hobbit archers who went off to war against Angmar and were never heard from again. Even then, we don't know if any of them considered themselves warriors by preference.
The Shirriffs perhaps
The position of Shirriff was a voluntary honor. There were a total of twelve Shirriffs at a time, three for each Farthing, though more could be appointed in time of need (as happened around TA 3001). Shirriffs were distinguished merely by a feather worn in their hats. They carried sturdy walking sticks, with which they kept "strange folks" and menaces at bay, giving them enough time to call any needed reinforcements.
Shirrifs when a guy in anything other than the usual cotton farm clothes walks through the border:
Well, the Bounders were Shirriffs, specifically they were the 'Outside Shirriffs' that kept the peace on the borders of the Shire. The 'Inside Shirriffs' were more apt to be settling a neighborly dispute over livestock or be found having a mug of ale on a meal break.
It says error 403