Just an addition for having a download of your Skype data.
I also had that great wish and after asking on another forum if anybody knew a possibility/program for that, I got the name of a good working program: Skyperious.
I downloaded version 5.6, did some tests that indeed downloaded the complete history of my most important contact since 2017-04-24. Apparently the older history isn’t available anymore, a pitty but for me this was already extremely important and quite a relief. I also have it running daily via the scheduler (I’m using Windows 10).
So perhaps you can import this in Jami, If so I would be happy to hear it 