Joseph Smith
born November 1801–November 1802
died 13–27 November 1837
  in Preston, Lancashire

Looking for baptism records within two years of 1802 (based on his age at death), and within twenty miles of Yealand Conyers, I have found two candidates:

Baptisms: 29 March 1801, Lancaster, St Mary
Joseph son of Richard & Mary Smith, Lancaster

Baptisms: 22 July 1804, Cockerham, St Michael
Joseph son of William Smith, Ellel, born June 28

These might not be the only Joseph Smiths at the right time in the right area, though, as I could not guarantee that all baptism records for the area have been transcribed (search was performed on Ancestry in October 2014). Of these two, the former looks the more promising, as he was married at the same church.

1832: Described as 'Bachelor of Yealand in the Parish of Warton' at the time of his marriage.

1833: A flax dresser, living in Yealand, near Warton, at the time of his daughter Rebecca's baptism.

1836: Harry Jack says: 'Grace's father's job as "flax-dresser" is from her baptism in the online Parish Records, as is their address in Spring Street. The two flax-spinning mills [Ribble Bank Mill in River Street, just off Bow Lane, and a little further away, the Leighton Street Mill] show up on the 1:1056 (5 feet to a mile) Ordnance plan of Preston, surveyed in 1847. Seeing them surprised me—I thought it was all cotton in Lancashire and I didn't expect to find linen mills in Preston, but there they are, albeit ten years after Joseph's death.'

1837: The LDS has a couple of records of the burial in 1837 of one Joseph Smith of Marsh Lane, aged 35:
residence: Marsh Lane
record title: England Deaths and Burials, 1538-1991
name: Joseph Smith / Joseph Smith P51c
gender: Male
burial date: 27 Nov 1837
burial place: Preston, Lancaster, England
age: 35
indexing project (batch) number: B03821-6 / B02973-4 / B02934-8
system origin: England-EASy
source film number: 1278756 / 94011
The name is right, the death is in the expected fairly tight range, the age is about what we'd expect (same as wife's), and the residence is the street where the family were living soon after.

1838: Harry Jack says that young Joseph's baptism record describes Joseph, sr as 'the late Joseph Smith, flax-dresser'.

1857: Occupation is given as hairdresser [more likely flax dresser!] on daughter Grace's marriage certificate.