I did a search of printed dictionaries from the early 20th century, discounting Internet sources as prone to regular errors and inconsistency. I found the following:
Pom-pom n. a machine gun of large size
Pom-pon n. an ornamental ball, as of feathers or ribbon[1]
Next,
pompom [From sound of the discharge] n. a one-pounder automatic Maxim gun (Colloq.)
pompon (F. pron. põn-põn' n. [Also pompom; <F. pompon an ornament, <pomp splendor, see pomp] an ornamental tuft of feathers, silk, etc. for a bonnet or hat
[2]
Then
pom'-pom, n. a one-pounder, quick-firing gun (from the sound).
pon'-pon, (F.)n. a tuft of feathers or wool on a shako or hat.[3]
And then this, from the academic journal Language published by the Linguistic Society of America in 2004:
"...This is apparent in patterns of speech errors, for which it has been widely established that consonants sharing greater similarity have an increased likelihood to participate in a slip of the tongue... Priming among similar segments within words is also made evident by phonologically based analogical pressure. Zuraw (2000) observes that segments in similar syllables are often rendered identical; English examples include pompon -- pompom, sherbet - sherbert."[4]
(Wikipedia has the ice cream "sherbet" under sorbet where in the section "Distinction from sherbet" there is a link to the Wiktionary definition of sherbert explaining that this is a common but still incorrect variant of "sherbet").
Lastly, from the Oxford English Dictionary, which I consider to be more reliable than most (given here slightly abbreviated):
pom-pom [Echoic.] 1.1 The name given during the South African war, 1899–1902, to the Maxim automatic quick-firing gun.
pompon, pom-pom Also pong pong, pomponne, pomˈpoon, pompom, ponpon, pompone.
[a. F. pompon (1725 in Hatz.-Darm.) a tuft, top-knot; of uncertain origin; possibly a colloq. deriv. of pompe', see pomp.] A jewel or ornament attached to a long pin.
- ^ William Dodge Lewis; Edgar Arthur Singer (1919). The Winston Simplified Dictionary: Including All the Words in Common Use Defined So that They Can be Easily Understood. Philadelphia, Pennsylvania: John C. Winston Company. p. 472.
- ^ William Dwight Whitney; Benjamin Eli Smith (1914). The Century Dictionary and Cyclopedia: The Century dictionary ... prepared under the superintendence of William Dwight Whitney ... rev. & enl. under the superintendence of Benjamin E. Smith. Century Company. p. 4614.
- ^ Charles Lamb (1908). Selected tales from Shakespeare [by] C. & M. Lamb, with extracts from the plays, prepared by A. Gardiner. p. 287.
- ^ http://www.jstor.org/stable/4489721 p. 488
It seems clear that the original word was the French pompon (no hyphen, one M, one N) and it looks like as the word was adopted into English that it was [erroneously] converted by some speakers into pompom for the morphological reasons given in the journal article. Though both forms are perhaps now "correct" in some sense, the primary English form chosen in reliable published sources (and discounting those like "Wordsmyth.com" that don't even spell the word "smith" correctly as inherently unreliable) seems rather consistently to be either pom-pon or pompon.
According to WP:COMMONNAME, even if the "No consensus" conclusion is eventually reached regarding the M vs. N issue, as the first non-stub version of the article title was one ending with the letter N and not the current one ending with the letter M, the earlier title (with or without the hyphen, which I view as largely irrelevant to this discussion) spelled with an N should be returned to.
Furthermore, while the policy given under WP:UE is meant to encourage the use of English spellings of otherwise foreign words in article titles and was used earlier to support a move of the article to its current location under pom-pom, the word "pompon" is an English word (as well as a French one, from which it is derived) and happens to be the historically correct English word (which pompom is not, unless you are talking about the gun, which we aren't): WP:UE is therefore not relevant in this instance.