Zip Archive With Limited Number of Files

You can use GNU parallel to do that as it can limit the number of elements to a job as well as provide a job number (for a unique zip archive name):

$ touch $(seq 20)
$ find . ! -name "*.zip" -type f -print0 | parallel -0 -N 5 zip arch{#} {}
  adding: 1 (stored 0%)
  adding: 10 (stored 0%)
  adding: 11 (stored 0%)
  adding: 12 (stored 0%)
  adding: 13 (stored 0%)
  adding: 14 (stored 0%)
  adding: 15 (stored 0%)
  adding: 16 (stored 0%)
  adding: 17 (stored 0%)
  adding: 18 (stored 0%)
  adding: 19 (stored 0%)
  adding: 2 (stored 0%)
  adding: 20 (stored 0%)
  adding: 3 (stored 0%)
  adding: 4 (stored 0%)
  adding: 5 (stored 0%)
  adding: 6 (stored 0%)
  adding: 7 (stored 0%)
  adding: 8 (stored 0%)
  adding: 9 (stored 0%)
$ ls
1   11  13  15  17  19  20  4  6  8  arch1.zip  arch3.zip
10  12  14  16  18  2   3   5  7  9  arch2.zip  arch4.zip

The option -N 5 limits the number of files to 5 per archive and is presented to zip in place of {}

The {#} (verbatim, not to be replaced by you during the invocation), is replaced by the job number, resulting in arch1.zip, arch2.zip etc.

The -print0 option to find and -0 option to parallel in tandem make sure that filenames with special characters are correctly handled.