Thanks!
Now, a brief feedback:
Tightening the saddle screw worked quite well. I had to detach the bridge though, in order to hold the aircraft nut firmly. As Jimmy, I used a small channel-lock plier for that. For the other end I used a 7/64 hex key. Moreover, I applied a bit of cleaner on the aircraft nut to make it go easier - that also helped with the procedure.
I can still move the saddle for adjustment, but the saddle is not wiggling anymore while playing - so the job was successful
Thank again for all you helpful advice.
Best,
Philipp
