I'd check with the local county/city to find out what the ordinances are ... usually you can trim anything encroaching on your property but some cities/states may vary in their laws and your area may have a law against that. Since his landscapers are coming onto your property to mow ... why not just ask them to trim the hedges away from side of the fence? If you do decide to do the trimming yourself, maybe you should take a few before and after (date stamped) photos for your records.
