Better picture at this website:
The PC5-141 cable you have found is in two parts, to enable an FM modulator to be installed between the aerial and the head unit. The lead was intended for newer Hondas which uses rectangular connectors.
But as you already have a round DIN connector on the end of your existing aerial lead, then it is reasonable to assume you only need to use the appropriate cable from this PC5-141 cable kit which would be inserted into the head unit.....
Perhaps contact the supplier to clarify which grey rectangular connector is associated with the black shrouded round DIN aerial inline female connector?
It's difficult to tell from the upper photo, but it looks to me that the round DIN female aerial connector is attached to the left-side grey male rectangular plug - which I guess inserts into the head unit. If I am right, then this would indeed resolve your aerial wiring issue.
Anyone else got an opinion?
There is no aerial amplifier to worry about for 2002 and 2005 Jazz according to the wiring diagrams from my Jazz/Fit service manual.