The 2nd link you provided says that John Waisanen was 23 years old at time of his execution in 1885, and from Finland. He had a wife and a child and had come from Hancock Minnesota three years previously.
Maybe this man - b. 1863 Finland on the 1885 census - he is listed with many other men - maybe jail? The census is usually taken in June. The execution was August 1885. https://familysearch.org/pal:/MM9.1.1/MQXT-3SR
name: John Weisenen
event place: Duluth, St Louis, Minnesota
age (expanded): 22 years
birth year (estimated): 1863
family number: 1380
volume: St Louis
gs film number: 000565754
You'll have to click on the link to see that he is listed with a bunch of other men.
You would have to look at the microfilm to see if it is jail in St. Louis County (Duluth), Minnesota
YOu should be able to get his death certificate from St. Louis county, MN