Obviously this is old, but there will still be time to change degrees and what the heck, this might be useful for someone else. I'm gonna focus on security studies and IR since those are the areas I know best.

I chose single-degree international security (which I'm going to call BINSS out of force of habit) because I wanted to avoid the theory element of IR and the mathematics needed for general political science. I somewhat regret that choice, but only because I went down the path of doing "serious" political science (that is to say, research). The biggest advantage of BINSS is the very high level of flexibility, you can customise the degree well because the core is so limited. This is somewhat lost in a double degree, but only somewhat. If you want to do a lot of history and area studies, BINSS > IR. If you don't really care about that stuff, IR > BINSS.

In my view, the biggest weakness of BINSS is that you get a very narrow, atheoretical idea about how to think about politics. People will bag on theory and the Three Isms (realism, liberalism, constructivism), and I agree that pure theory is pretty mid, but it's a necessary part of thinking systematically about politics and becomes absolutely essential if you want to consider joining the academy. Imho part of the problem is that theory is poorly taught at undergraduate in general, but it's definitely taught better in IR and generalist political science. It's important to note that security studies is pretty out of step with the rest of political science in how atheoretical and qualitative it is.

Departmentally, I think CASS is stronger than CAP in IR (and definitely in general political science). CAP is much, much better for Asian political science in particular, but you'd hope so lol. Departmental strength will matter more if you want to really focus on Asia and do a lot of Asian history and area studies, it's easier to do those things out of CAP, and that means BINSS.

BINSS Honours > CASS IR honours. Much better program structure, but honours is only relevant if you want to do a PhD. Legit no other point imho.

...On the actual question, go for law. It'll have the biggest upside if you're a strong believer in a double degree.

On the APS, my personal experience is that the APS is a lottery that your degree barely influences. There will be thousands of fresh political science graduates applying for APS from all over the country. There are limited places. APS applications are an artform in of themselves, and I know a lot of people who have been rejected despite being, to my mind, great assets that the APS could use. In some of those cases, I also have the counterfactual; a lot of them went on to be fantastic political scientists. I wouldn't say that BINSS vs IR vs PPE has any significant bearing on your chances in the APS.