[Merry]

First of all it's a good idea to record Cicily's siblings, in order to hopefully find the correct marriage for Richard. These are from Lancs OPC:

Baptism: 29 Apr 1798 St Thomas, Upholland, Lancashire, England
Mary Walker - Daughter of Richard Walker
Abode: UpHolland
Occupation: Collier
Register: Baptisms 1789 - 1812, Page 27, Entry 14
Source: LDS Film 1657546

Baptism: 11 May 1800 St Thomas, Upholland, Lancashire, England
Betty Walker - Daughter of Richard Walker
Abode: UpHolland
Occupation: Collier
Register: Baptisms 1789 - 1812, Page 33, Entry 9
Source: LDS Film 1657546

Baptism: 6 Jan 1803 St Thomas, Upholland, Lancashire, England
Cisely Walker - Daughter of Richard Walker
Abode: UpHolland
Occupation: Collier
Register: Baptisms 1789 - 1812, Page 40, Entry 33
Source: LDS Film 1657546

Burial: 2 Feb 1803 St Thomas the Martyr, Up Holland, Lancashire, England
Cicily Walker - Daughter of Richard Walker
Abode: Upholland
Register: Burials 1790 - 1812, Page 1, Entry 17
Source: LDS Film 1657546

Baptism: 25 Mar 1804 St Thomas, Upholland, Lancashire, England
Cecily Walker - Daughter of Richard Walker
Abode: UpHolland
Occupation: Collier
Register: Baptisms 1789 - 1812, Page 45, Entry 24
Source: LDS Film 1657546

This could be his marriage:

Marriage: 31 Oct 1797 All Saints, Wigan, Lancashire, England
Richard Walker - (X), Upholland
Ellen Gaskell - (X), Upholland
Witness: Wm. Bancks; Henry Fishwick, (X)
Married by Banns by: John Fawel
Register: Marriages 1790 - 1803, Page 188, Entry 752
Source: LDS Film 1885689

Next thought is, less than ten years worth of children after the marriage. Was that because Richard's wife was older, or because she (or Richard) died, or because they moved to a different parish or had come from a different parish in 1798 (making that 1797 marriage less likely)?

Also, you said "1803 birth" note that 1803 was the year the child was baptised, not necessarily when they were born. The Cecily baptised in 1803 died in 1803, so your Cecily was baptised in 1804.