Those S&S cable splitters only split the CABLE, not the cable housing. They can only be used in a section of bare cable that is exposed with no housing. Look at the photo again.....see how it's just bare cable there? The cable housing ends at the frame's cable stops.
The best way to switch out your bars would be to remove the brake caliper from the fork. Your riser bars would have a full brake assembly, consisting of a brakelever/brakecable/brakecaliper. And your other handlebars would have another brakelever/brakecable/brakecaliper.
When you want to switch the bars, just loosen the stem and remove the brake caliper mounting bolt.....switch the bars and install the brake caliper that is dangling down from the other bar's cable....