I'm not sure why you're avoiding the AND clause. It is the simplest solution.
Otherwise, you would need to do an INTERSECT of multiple queries:
SELECT word FROM table WHERE word NOT LIKE '%a%'
INTERSECT
SELECT word FROM table WHERE word NOT LIKE '%b%'
INTERSECT
SELECT word FROM table WHERE word NOT LIKE '%c%';
Alternatively, you can use a regular expression if your version of SQL supports it.