I am late again with my reply, I hope you do not get that wrong !
Finally I had the occasion to insert your code and I can report happily
that it's all working perfectly now ! Evrything gets downloaded properly
just at the length of file as it should. Thanks a lot for your help !!

In order to provide all relevant information, in case someone looks this up:
I had to find out, that after everything was solved, at least some windows-machines
Would react strangely when downloading the zipfile. Strangely here means
that there was no error message, yet the zipfile was shown as empty
when handled by the operating systems (windows 8) functions.
Accessing the files with Winzip showed the files were not empty at all
but winzip issued a warning message regarding the paths given in the
Zipfile, starting with two leading dots. So I removed the paths from the
Zipfile and everything is ok since then.

Once again : thanks a lot

Cheers

Is it the header section in which you expressively specify the length of file, that solved the issue ? If not: what was it ?

I'm not sure myself, it's been a good ten years since I last had to deal with CGI. It should have worked without the content-length header, so - charset => 'binary' perhaps? Well, glad to hear it works now :)