bash iterate file list, except when empty

In bash, you can set the nullglob option so that a pattern that matches nothing "disappears", rather than treated as a literal string:

shopt -s nullglob
for fname in *.zip ; do
   echo "current file is ${fname}"
done

In POSIX shell script, you just verify that fname exists (and at the same time with [ -f ], check it is a regular file (or symlink to regular file) and not other types like directory/fifo/device...):

for fname in *.zip; do
    [ -f "$fname" ] || continue
    printf '%s\n' "current file is $fname"
done

Replace [ -f "$fname" ] with [ -e "$fname" ] || [ -L "$fname ] if you want to loop over all the (non-hidden) files whose name ends in .zip regardless of their type.

Replace *.zip with .*.zip .zip *.zip if you also want to consider hidden files whose name ends in .zip.

Use find

export -f myshellfunc
find . -mindepth 1 -maxdepth 1 -type f -name '*.zip' -exec bash -c 'myshellfunc "$0"' {} \;

You MUST export your shell function with export -f for this to work. Now find executes bash which executes your shell function, and remains at the current dir level only.

set ./*                               #set the arg array to glob results
${2+":"} [ -e "$1" ] &&               #if more than one result skip the stat "$1"
printf "current file is %s\n" "$@"    #print the whole array at once

###or###

${2+":"} [ -e "$1" ] &&               #same kind of test
for    fname                          #iterate singly on $fname var for array
do     printf "file is %s\n" "$fname" #print each $fname for each iteration
done                                  

In a comment here you mention invoking a function...

file_fn()
    if     [ -e "$1" ] ||               #check if first argument exists
           [ -L "$1" ]                  #or else if it is at least a broken link
    then   for  f                       #if so iterate on "$f"
           do : something w/ "$f"
           done
    else   command <"${1-/dev/null}"    #only fail w/ error if at least one arg
    fi

 file_fn *