The best place to confirm the relationship between the two Georges would be through parents' names on their death cert (1887 and 1897).
I am having a problem establishing the nephew relationship

Bishop George's parents are showing as George Rigg and Isabel Caven on the link above and we know his birth year was 1814.
Father George's parents I think were a James Rigg and Eliza Stephenson. His age at death in the Summer of 1897 shows as 36. I am wondering whether this may be his birth entry:
GEORGE STEPHENSON RIGG Birth: 06 AUG 1860 Stornoway, Ross And Cromarty
Parents: JAMES RIGG and ELIZA STEPHENSON
The parents and children in 1861:
James Rigg 36, farmer b. Kelton Kircudbright
Eliza Rigg 34 b. England
Mary Rigg 13 b. Annan, Dumfrieshire
Elenor Rigg 4 (likely 11, aged 1 in 1851) b. Coll, Rossshire
Eliza Rigg 9 b. Coll, Rossshire
Jessie Ann Rigg 7 b. Coll, Rossshire
James Rigg 2 b. Coll, Rossshire
George Rigg 8 months b. Coll, Rossshire
Address: Coll House, Stornoway
The closest I can see for James Snr. above in 1841, with the usual problem of the 1841 census in that no relationships are included within households:
Thomas Rigg 55, farmer
Mary Rigg 40
Nicholas Rigg 20
Elisabeth Rigg 20
John Rigg 15
James Rigg 15
Catterina Rigg 12
Lucy Rigg 10
Barbara Rigg 8
Rev. Thos John Strain 30, Catholic Clergyman
Address: Midkelton Farm House, Kelton Kirkcudbright
Monica