George Ade also uses the expression "fresh drummer" in "The Fable of The General Manager of the Love Affair Who Demanded a Furlough," in Forty Modern Fables (1901):
"... If Cupid had his Way, every Marriage Service would be enacted in the still Moonlight, with no $10 Preacher to give the Cues, and only the Peeping Stars as Witnesses. The Young Couple would repair at once to a Lodge in some Vast Wilderness, eighty-five Miles from a Hotel Clerk or a Fresh Drummer. But as I am telling you., Love has no Voice during the so-called Festivities. When you begin to Frost the Cakes and hang Smilax on the Chandeliers, I [Cupid] fly the Coop."
According to James Maitland, The American Slang Dictionary (1891), fresh had the following slang meanings in the late 1800s:
Fresh, slightly intoxicated.
Fresh (Am[erican]), said of a man who thinks he knows everything and who talks freely and pushes himself forward.
and drummer had this meaning:
Drummer (Am[erican]), a commercial traveler.
J.S.Farmer & W.E. Henley, Slang and Its Analogues Past and Present (1891 & 1893) offers similar assessments of the two words;
Drummer, subs. ... 3. (general).—A commercial traveler; also AMBASSADOR OF COMMERCE or BAGMAN ... {Cf. DRUM = a road; and old-time pedlars announcing themselves by beating a drum at the town's end.} [Latest cited example:] 1885. G.A. Sala, Daily Telegraph, 14 August, 5, 3. Among whom were conspicuous sundry drummers or representatives of American commercial firms, bound for Australasia, there to push their wares.
Fresh, adj. ... 3. (Old English and modern American).—Inexperienced, but conceited and presumptuous ; hence, forward, impudent.
It thus appears that by "some fresh drummer rubbed it [the town name of Tomahawk, Wisconsin] out," Ade meant something like "an impudent traveling salesman single-handedly erased the town's name from the map (where it had been scarcely recognized by the wider world on account of its insignificance)"—the implication being that the place was so innocuous that no one would have noticed if someone had come along and reported, as a joke, that it didn't exist.
Apparently, for Ade, a "fresh drummer" was a byword for the sort of arrogant blowhard who could ruin a honeymoon just by being within 85 miles of it or who could take it upon himself to erase a tiny town from the map on a whim.