First: the passenger list you found must be for the guy first suggested by Maggie: "Karl Johan Nilsson, born 1874-12-10 in Kroppa, Värmland. Leave home 1892-04-26, destination N. Amerika. He travels alone and would most probably left Sweden from Gothenburg." This is the wrong guy - not so strange, considering how common the name is. Census data about immigration years are notoriously vague - for your Carl Johan they suggest 1891, 1890 and 1889.
Now, among the fourteen emigrating Carl Johan Nilsson-s pulled out by Maggie, there was ONE with a father Nils Peter Persson, the other fathers were Nils Something-else. Persson and Pettersson at that time were still pretty much interchangeable in Sweden, and would certainly have appeared as Peterson in the US (this is one of those I-should-have-known things for me; I lokked only for Pettersson/Peterson).
The Karl Johan Nilsson with Nils Peter Persson as a father was born in Tuna parish, Kalmar county, 12 July 1872. He is actually the closest among the fourteen to the birth date you have for your Charles John Nelson. One always has to expect transcription errors in birth dates along the way when people move (even within Sweden). July turning into June is a minor error in comparison to what you may find. It's also kind of reassuring that he came from the same county as his wife - people do that a lot of the time, marry somebody who "sounds right" (have the same dialect) - although, of course you'll also find true melting-pot marriages.
All in all, I think this is your guy - now the challenge is to find his arrival in the US. He moved out from his home parish March 16 1891.