The name doesn't appear on the Register of Swiss Surnames (
http://www.hls-dhs-dss.ch/famn/index.php ) but the alternate spelling Arrigo appears in Caneggio as having been there since before 1800.
There is very limited availability of Swiss records online. You can order microfilms of the Caneggio parish records if you have access to a family history centre:
https://familysearch.org/search/catalog/468490?availability=Family%20History%20LibraryFrom where do you have that his father was also Louis? I can see the Louis of a similar age in the census, presumably the brother you mention. I see there are baptisms on familysearch to a Louis Arigho + variants and both "Leotine" and "Mary Estella", however looking at the children on the census I think these are all the same person, appearing as Estella in 1911.
Also, sites outside familysearch give different details, example,
http://churchrecords.irishgenealogy.ie/ has the baptism of Mary Ellen Winifred "Arigi" in 1875, and gives her parents as "Luis" and "Estella Leontina", rather than "Mary Estella" as on familysearch. (This latter appears to be accurate to the images of the Catholic records which can be found on registers.nli.ie )
http://registers.nli.ie/registers/vtls000639791#page/69/mode/1upThis looks to be the (church) marriage of John and Ellen Ryan. Gives his parents names as Baptiste and Constanza - I think their residence is just given as 'Switzerland'.
Hard to know where Louis and "Estella" may have married - Caneggio was very small at the time, around 400 inhabitants, and the chances are that the brothers had moved away to find work, possibly over the border into Italy or across to France.
In 1911 Estella says she has been married 46 complete years, five children with five living, putting their marriage circa 1865 although the first trace of children to them in Ireland that I can see is 1872.