Both caps should have a manufacturer's mark in them. This might give a clue. If the visorless one is indeed a Württemberg cap, then it would not belong with this tunic. The visored cap appears to have a Hanseatic reservist cockade, as Ron has mentioned, so it would be a likely candidate. The FAR.45 was in the IX.A.K., which included Hamburg, Lübeck and Bremen.
Chip