Well, if he's really offensive just play a little more defensively. Shield grab is really fast, especially if you power shield attacks. Also, if you are getting wrecked trying to edge guard him, again try and play a little more defensively. I mean, still jump and fake like you are going to hit him, but don't get close enough to get hit, that way (best case scenario) he starts to run low on up-B and is forced into a bad position.
But yeah other than playing more defensively (Brawl is a defensive game IMO) just make you sure you really punish him when you get a grab off, because you probably won't get many.
Again, feels wierd giving advice