The Wikipedia entry for "Good Old Mountain Dew" indicates that the song's lyrics appear in two American versions—a ballad-like song from 1928 by Bascom Lamar Lunsford, and a less story-like narrative from 1935—with a possible further connection to an Irish song called "The Rare Old Mountain Dew" from 1916. The "sweet-smelling phew/pew/pu" stanza appears to have been a somewhat later addition, as it doesn't appear on any of the earliest recordings of the song listed on the Fresno State Folklore Ballads page.
The version recorded by Lulu Belle and Scotty in 1939 and by the Delmore Brothers in 1940 include stanzas featuring "the preacher" and "Mr. [Franklin] Roosevelt" but no appearance by Aunt Jill/June/Maroon and her perfume. The earliest recordings with the "sweet-smelling pew" line I've found is the version sung by Grandpa Jones in 1947 and by Kenny Roberts not earlier than 1949. Both Grandpa Jones and Kenny Roberts delivered their performances in a somewhat jokey way, lending credence to the idea that "sweet-smelling pew" was used for comic effect.
I haven't been able to uncover other instances—in Google Books or elsewhere—of phew/pew/pu being used to describe a smell that isn't unpleasant. It therefore seems likely that the intended effect of the phrase "sweet-smelling pew" in "That Good Old Mountain Dew" is to sound humorously self-contradictory, equivalent to "sweet-smelling stench" or "sweet-smelling stink."
An extended look at 'phew', 'pew', and 'P.U.' (only marginally related to the OP's question)
As Hot Licks indicates in a comment above, the approved spelling in the OED and in Merriam-Webster for the word spelled pew in the OP's question is phew. The online Oxford Dictionaries' definition of phew is quite narrow, but it does identify the origin of the word rather neatly:
phew exclamation informal Expressing a strong reaction of relief: 'phew, what a year!'
Origin: Early 17th century: imitative of puffing.
Merriam-Webster's Eleventh Collegiate Dictionary (2003) has this:
phew \ a voiceless bilabial fricative usu followed by a voiceless (y)ü or ue sound; often read as 'f(y)ü\ interj (1604) 1—used to express relief or fatigue 2—used to express disgust at or as if at an unpleasant odor
And the Compact Edition Oxford English Dictionary, volume 2 (1985), has this:
Phew ... [Representing the action of puffing or blowing away with the lips] A vocal gesture expressing impatience disgust, discomfort or weariness.
Like MW, the OED gives a first occurrence date of 1604 for the word, pointing to an instance where the word is actually spelled pheut. From John Marston, The Malcontent (1604):
Malvole. 'Tis gone ; 'tis swallowed like a mineral ; some way 'twill work ; pheut, I'll not shrink : He's resolute who can no lower sink.
Oddly enough, the word spelled as phew appears in the same play, just one scene earlier:
Ferrardo. I study languages. Who do'st think to be the best linguist of our age?
Malvole. Phew! the devil ; let him possess thee ; he'll teach thee to speak all languages most readily and strangely ; and great reason, marry, he's travell'd greatly in the world, and is every where.
Unfortunately, the OED doesn't provide an early example (or any example at all, actually) in which phew is used in the specific context of a reaction to a bad smell; and of course, MW never bothers to identify when secondary meanings of a word emerge, so neither reference is terribly helpful with regard to determining using phew in reaction to a bad smell first arose. Nor is the Online Etymological Dictionary of much use:
phew vocalic gesture expressing weariness, etc., attested from c.1600.
In a Google Books search, the earliest relevant matches I could find were from George Darley, Sylvia; or The May Queen (1827):
Stephania and Roselle. Alas! Alas! He is growing as small as a tom-tit!
Andrea. Son of my father! They look like two white mice at the door of a trap!—Farewell, hostesses!—good-bye!—O sad! O marvellous!—they are not the size of their noses!—Phew! I begin to smell brimstone and pitchforks!
And later in the same play:
Andrea. My stars! What a—phew! he [Ararach, King of the Fiends] has left after him : like the last sighs of ten thousand expiring candles. It is enough to smother all the hives in Sicily. Now if he would only be satisfied to live like a man of reputation, he might earn an honest livelihood by travelling as a sulphur-merchant to the North (where, I am told, there is a great demand for that article), or by selling matches through the streets,—two bundles for a halfpenny.
The variant spelling pew (as applied to unpleasantly odoriferous objects) may owe its popularity, in part, to the cartoon character Pepé Le Pew, the amorous French skunk, who debuted in the Warner Brothers cartoon "Odor-able Kitty" in 1945, according to Le Pew's Wikipedia article, and whose name appears in the title sequence of his second cartoon, "Scent-imental Over You" in 1947.
P.U. may have arisen somewhat later. Here is the entry for that term in Harold Wentworth & Stuart Flexner, Dictionary of American Slang (1960):
P.U. [or] p.u. 1 Phew, said on smelling a bad smell, as something rotting. Colloq. An exaggerated pronunciation of "phew." 2 "It stinks."
In our car travels through rural Texas during the late 1950s and early 1960s, the custom of the children in my family was to sing out in unison, whenever the aroma of skunk wafted through the open windows of the car, "P.U. skunk!"