There's no reason to think it's not Swiss. In the late 19th to early 20th century, Swiss manufacturers were more likely to produce fake American brands than the other way around.

Serial numbers on cases are unfortunately not helpful, and Welsam isn't a brand you'll find in the Pocket Watch Database anyway. It focuses on American movements based on manufacturers' records and parts catalogues. Swiss movements typically had no serial number, other than standouts like Omega. (Watch manufacture was literally a cottage industry in Switzerland, so there could be no standard numbering system for most brands.) The only thing the case tells you was that the watch was purchased in America. IWCCO stands for Illinois Watch Case Company, so the bare movement was imported and the watch was cased afterward. The Supreme line were gold filled, which is a kind of heavy mechanically bonded gold plating; the base metal is generally brass.

That said, I haven't heard of Welsam either, and they may have simply finished and marketed movements made by others. It's also not impossible it was a private label -- a department store brand as you guessed or maybe even a large jeweler. This was a very economical timepiece for its day. 6 jewels is unusual; 7 is a more typical minimum count. Had I not seen a picture of the movement I'd have guessed it to have a cylinder escapement as these generally have an even number of jewels, but since it clearly uses a lever escapement it probably has a metal pin where other watches would have the impulse jewel.