I think designating power weapons in the list is a good idea too. But really I don't think you'd ever notice if someone was cherry-picking at deployment, nor is there really anything you can do about it. Possibly at a tournament setting (since the same list is used every game it seems reasonable to expect the same models to be used!) but otherwise, what are you going to say?
"This guy has a power maul?"
"Yep, right there on the model."
"Is that on your list?"
"No, it just says power weapon."
"Weren't you using a guy last week that had a power sword!?"
"Uh... yeah? So what?"
Really, there's not going to be an easy way to tell if he's breaking out the power mauls for you because you play IG or power axes if you put down terminators (well, it might be a bit obvious if it's a whole squad of chaos terminators) or whether it's just a coincidence.
Ultimately it's a pretty minor advantage/disadvantage so it probably isn't worth getting upset about. Obviously with a regular group you can just agree to have the specific weapon types down on your list or at least pick the models before you know what you're facing.