> it's just renaming files to .shtml :(

Ensure you didn't broke the sed line:

#!/bin/sh
#
test -f "$1" || exit 1
# One single line here:
cat "$1" | \
sed -e \
"s/\([\"']\)\([^\"']*\)\(\.html\)\([\"']\)/\1\2\.shtml\4/g" 
\
> "${1%.*}.shtml"
# (End of long line)
rm -f "$1"

This should definitely work if you have sed and bash 
installed