Wow folks, Thank you so much for you valuable replies
.
Very important and good tips an trick about the size of the battery and even more about the removal.
Didn't got that much time last days to find an appropriate battery in an online shop, with they deliver to Switzerland, but first of all I have to get the replacement now. (Saw some appropriate models in size, but very poor mAh (350/750 an so)).
After I get the replacement, I will continue the project of documentation the whole process. Of course I will try to remove the battery with the hard plastic card (CC?) and also the fishing wire.
I thought also to disassemble the device a litte bit more, to remove the whole battery surrounding plastic core.
This could enable to work with the removal fully in horizontal level as screen is positioning. Also the idea of a very thin saw wire could maybe a possibility. Or warming the nylon/wire to about 40/45°C before working.
I'll keep you updated, as soon I found a battery an it get delivered.
Best regards and thank you again!
Matthias