Looking for possible siblings, could this be one?
Micheal Welch
Birth c1819, Ireland
1860 Elk, Delaware, Iowa census -
Michael and his family with first child, Mary Ann, born c1842 in Illinois
I have not continued the search. Michael could be a wild goose chase but I thought I would mention him.
ADDED: Coincidence that John and Michael were both in Elk
You may already have the following information.
M. Welch, farmer, residence section 35 in Elk Township. I don't know if it was the same person as Michael Welch.
J. Hennessy, renter, residence section 27.
(Biographical Township Directory, Elk Township, Delaware County, Iowa History Center. Sourced from "History of Delaware County, Iowa" pages 625-636)
iagenweb.org/delaware/history/1878/632-636.htm
Unfortunately no biographical information for M. Welch or J. Hennesy is included. There's biographical information about some others on the list. Among those with biographical info are a few Irish-born residents, Henry Barr, James Fitzpatrick, Cornelius Kennedy, Abram Parliaman and a man named Young. Each took a different route from Ireland to Iowa. Some names in the directory were early settlers in 1840s & 1850s.
Elk Township and Greeley were mentioned in extracts from "History of Delaware County, Iowa and Its People", published 1914, which are online. Some include names of early settlers in 1840s & 1850s. Greeley was a village until railway arrived in 1870s. Greeley population in 1914 was 400.
Considering the apparently small populations of Elk Township and Greely in 1860, I think Michael Welch is a lead to follow.