An “Arkansas toothpick” is a jocular name for a dagger-like blade, similar to a Bowie knife. It was famous for ending fights, not picking teeth. “Arkansas tooth pick” was cited in the American Traveller (Boston, MA) on April 29, 1836.
 
A resident of Arkansas was called a “tooth-picker” in 1843, and “Arkansas, Tooth Pickers” was included in an 1843 list of national nicknames. The “Toothpick” or “Toothpicker” nickname was only infrequently used to describe a person—“Arkansas toothpick” is still used to describe the blade—and is of historical interest today.
 
   
Wikipedia: Arkansas toothpick
In modern terminology the Arkansas toothpick is a heavy dagger with a 12–20-inch (30–51 cm) pointed, straight blade. The knife can be used for thrusting and slashing. James Black, the inventor of the Bowie knife, is credited with inventing the Arkansas toothpick.
 
There was no consistent distinction made between Bowie knives and Arkansas toothpicks in the mid-19th century. There were enough occasional distinctions to shade any dogmatic statement of equivalence. Americans were observed to use pocket knives to clean their teeth in the era, so the Arkansas toothpick term may predate the Bowie knife. There is some (debatable) basis for claiming that Arkansas toothpicks were designed for throwing.
 
(Oxford English Dictionary)
toothpick, n.
A bowie-knife: also Arkansas toothpick. U.S. slang.
1862   J. R. Lowell Biglow Papers 2nd Ser. i. i. 19,  I didn’t call but jest on one, an’ he drawed toothpick on me, An’ reckoned he warn’t goin’ to stan’ no sech doggauned econ’my.
1881   A. B. Greenleaf Ten Years in Texas 27   With..an Arkansas ‘toothpick’ suspended to a raw-hide belt buckled around their waists.
   
29 April 1836, American Traveller (Boston, MA), “Selected Summary,” pg. 2, col. 2:
Bird was executed at New Orleans April 8th, for the murder of Harvey. The frequent murders there and elsewhere in the south and west generally, arise from the habitual practice of carrying arms, such as the Bowie knife, Arkansas tooth pick and pocket pistol.
 
Chronicling America
9 August 1836, Southern Telegraph (Rodney, MS), pg. 4, col. 4 ad:
... Bowie & Crockett knives and Arkansas tooth-picks, ...
 
Chronicling America
27 September 1837, Vermont Telegraph (Brandon, VT), pg. 3, col. 5:
ALABAMA—We have seen a copy of the law of this State against Bowie knives and Arkansas tooth-picks; and if legal enactment can prevent their use, this will answer the purpose.
 
Google Books
5 August 1843, Supplement to the Courant (Hartford, CT), pg. 128, col. 3:
(State nickname list from the New-York American.—ed.)
Arkansas, Tooth Pickers.
 
24 August 1843, New-Hampshire Patriot and State Gazette (Concord, NH), “Seven Thunder Storms in a day,” pg. 4, col. 3:
After running down the Mississippi and making a flying trip among the Arkansas tooth-pickers, it has suddenly appeared among the granite hills of New Hampshire. (...)—Geneva Courier.
 
Google Books
December 1846, The Eclectic Magazine, “American Nicknames,” pg. 567, col. 2:
Arkansas…The Toothpickers
 
Google Books
13 December 1856, Notes and Queries, “Nicknames of American States” by St. John Crookes, pg. 475, col. 1:
Arkansas, the Toothpickers, and the Bear State.
 
25 July 1864, Indianapolis (IN) Daily Journal, ‘National Nick-Names,” pg. 4, col. 2:
Arkansas…Toothpickers
 
22 March 1866, Louisville (KY) Daily Journal, “Nicknames,” pg. 1, col. 4:
Arkansas, Tooth Pick State.
(...)
The natives of these States are:
... Arkansas, toothpicks; ...
 
7 April 1866, The Daily Cleveland Herald (Cleveland, OH), “Geographical Nicknames,” pg. 2, col. 2:
... Arkansas, Tooth Pick State; ...
 
Google Books
15 November 1877, New-England Journal of Education, “Sobriquets of the States and Their Inhabitants,” pg. 221, col. 3:
Arkansas, Bear State, Bears. Toothpickers.
 
Google Books
U. S.
An Index to the United States of America
Compiled by Malcolm Townsend
Boston, MA: D. Lothrop Company
1890
Pg. 75:
NICKNAMES APPLIED TO THE PEOPLE OF THE STATES.
(...)
Arkansas…Toothpicks...Playful allusion to the Bowie knife; in frontier times it was spoken of as an “Arkansas toothpick.”
 
OCLC WorldCat record
“They’ll do to tie to!” : the story of Hood’s Arkansas toothpicks, Third Arkansas Infantry Regiment C.S.A.
Author: Calvin L Collier
Publisher: Little Rock, Arkansas : Butler Center Books, 2015. ©1959
Edition/Format:   Print book : English : First edition