Harald, you're right of course, but I don't see that it matters. There are two different questions here. First, is Odin as Sigge an authentic, pre-Christian tradition? Of course not. We already know that.
Second, where did anyone ever get the idea? That's the really interesting question.
Over and over, in 18th and 19th century sources I'm seeing variations on the statement "Odin founded Sigtuna and named it after himself." In fact, Sigtuna has an entirely different etymology, so this statement ins't a clue to the truth. It's a clue to the belief at that time.
We already know Scandinavian historians did not "re-discover" Icelandic literature until relatively late in the game. Say, the late 18th or early 19th centuries. So, the source for Sigge is most probably outside the sagas and not nearly so old.
We also know that modern experts do not believe there was ever a uniform system across the north -- that the names and relationships of the gods varied across different regions. The Prose Edda (13th century) says, "Odin's third son was called Sigi; his son Rerir; this pair ruled over what is now called France, and the family known as Völsungar came from there." So that's another piece of the puzzle.
I thought the most likely source for Odin = Sigge would be Johannes Magnus (Archbishop of Uppsala), Historia de omnibus Gothorum Sveonumque regibus (1554). But, no. He has two Sigges in his king list and one Odin. That might be worth looking into, but it's not an obvious source.
https://sv.wikipedia.org/wiki/Historia_de_omnibus_Gothorum_Sveonumq...
Instead, I find this statement at Swedish Wikipedia: "I den likaledes euhemeristiska historiesynen på 1600-talet framfördes av Olof Verelius och Johan Peringskiöld[17] åsikten att Oden hade en historisk förebild som de gav namnet Sigge Fridulfsson."
In other words, the idea of Odin as Sigge goes back to Olof Verelius and Johan Peringskiöld[ in the 17th century.
https://sv.wikipedia.org/wiki/Oden
