I think Hammar arrived in Våxtorp not to long before he married Gyllensvärd in 1822. Maybe he came 1820-21? It would be perfect if there was "flyttlängder" for those years, but it doesn't seem to be any.
Hammar was 43 years old when he married Gyllensvärd. He must have left a lot of clues where ever he was before he came to Våxtorp. Somewhere in Västergötland, but that's a big place. Maybe Habo as stated in the starting post, Habo is at least partly i Västergötland. And there seems to be many "Hammar" around Jönköping, so maybe there was some in Habo also.