Your boyfriend is either into bestiality or just uses your dog as his preferred method of cleaning his body. In other words, he may not be getting sexual satisfaction out of letting the dog lick his manlihood. Instead, he may be using the dog out of practicality–like a soggy, wet, flea-infested,sponge–rather than anything else.
If he does enjoy the dog sexually, there is a good chance that he will be able to tell the difference between you dressed up like a puppy and the real thing. I mean, suppose all of a sudden you became a lesbian and your boyfriend dressed up like a girl for you, would that work? Not likely.
As far as talking to him without shaming him goes, there is really not much you can say that won’t horrify him, so either accept this quirk of his or move on.
One thing, If you do decide to stick with him, you may want to research inter-animal diseases you are prone to receive from your boyfriend. It’s always good to play it safe.