Applescript character count in words with combining diacritics
I did a bit of experimentation, and I get varied results. Fortunately, one of those results was 4. I did this by outsourcing the calculation to Python:

on run {input, parameters}
    set var to "wx̀y"

    set output to (do shell script ¬
"python - &lt;&lt;EOF
# -*- coding: utf-8 -*-
print len(u'" &amp; var &amp; "')
EOF")

    return output
end run