OED Online suggests 'sprauncy' (slang) is "perhaps related to dialect sprouncey cheerful (Eng. Dial. Dict.)". The English Dialect Dictionary, in turn, gives a definition of 'sprouncey' garnered from The Ancient Language and Dialect of Cornwall (F.W.P. Jago, 1882):
cheerful, jolly; slightly intoxicated.
The phonetic resonance of 'sprouncey' in 'sprauncy' is clear. The semantic echo of "cheerful, jolly; slightly intoxicated" in "smart or showy in appearance or sound of voice" (OED Online), however, is nowhere near as definite, but such a semantic shift is a potentially likely development in the 70 years intervening between the documented appearance in the dialect of Cornwall and the use of 'sprauncy' first attested from 1957 (as remarked in a comment on another answer, and likewise as given in OED Online).
Searches for the forms 'sproncy' and 'sprauntsy' (as listed in OED Online) in readily available online corpora produced little. Both forms appear in The New Partridge Dictionary of Slang and Unconventional English (Eric Partridge, 2006; also found in related editions):
sproncy; sprauntsy; sprauncy adjective
showily dressed; fashionable; showy UK, 1957
- It was sproncy to go to South London and sleep with a Jamaican.
— Ben Sonnenberg, Lost Property, p. 160, 1991
- [T]he main focus for the Lib Dems must be to hold off and challenge the newly sprauncy Tories.
— The Guardian, 3 March 2004
The same reference documents a verb form, 'spronce':
spronce verb
to show off, especially by your choice of clothes UK
- Spronce was a word much used by girls in London then [the 1960s].
— Ben Sonnenberg, Lost Property, p. 160, 1991
'Sprauntsy' did not garner any other significant search hits in Google Books or Hathi Trust. 'Sproncy', however, was found in early 20th Century volumes of The American Kennel Club Stud-book, beginning in 1901 with this entry:
SPRONCY (63,825).—E. E. Bush, Caro, Mich. Breeder, D. W. Titmus, Fowlerville, Mich. Whelped March 15, 1900; orange and white.
The 'sproncy' form also appears in The Vineyard (September, 1920), in a story titled "Billy Barnicott" (Greville MacDonald), where it is glossed, possibly by an editor or the author, as 'excitable':
They harnessed the black, headless creatures to the bier and then muffled their hoofs with feather-bags—" which showed," argued the boy, "they was live an' sproncy (excitable) moilses (mules)..."
'Sproncy' in the sense of 'excitable' seems unrelated, or at best obliquely related, to the earlier "cheerful, jolly; slightly intoxicated" and the later "smart or showy in appearance or sound of voice" senses.