For most of your normals you better make sure they connect As Dudley pretty much can punish any whiffed standing normal and most of your crouching normals you have. It will hurt alot too. He can keep you out well if he knows what normal you'll use too. Stand MP and Cr. LK are the least likely to be tagged if whiffed. Since Dudley has to space himself right for his Stand HK to avoid a damaging trade for your Standing MP and still react to a whiffed cr.LK right. So they're most preferable for poking against Dudley. Even then, there will be a chance for a parry/universal overhead your way.
If you jump forward near Dudley, he can forward dash under whatever attack you intended to doing and possibly punish you for it.
Dudley can react to your forward dash and backdash quite good with Standing HP if he sees it.
You'll see quite a lot of work your way to get close to Dudley and any clever mindgames for you to win this.