Guess I'll answer my own question!
I beat Pokemon Dream Radar and I can confirm that you don't need the R button to beat the game. In fact, there's only 1 button needed to play the game through to the credits: the A button, which is used to fire the beam. The d-pad and B button are used for menu navigation, but you can just use the touchscreen for that purpose if you really need to.
So yeah, you can play Pokemon Dream Radar with just the A button, and can obtain Swablu, Driftloon, Riolu, Munna, Sigilyph, Igglybuff, Shuckle, Staryu, Porygon, Ralts, Bronzor, Togepi, Smoochum, Spiritomb, Rotom, and the forces of nature.
HOWEVER, there's some bad news. A little known fact about Dream Radar is that there are some cheat codes that unlock extra Pokemon. These codes are entered on the start menu, and they require several buttons to be pressed. These codes vary depending on whether you live in Japan or someplace else. I'm just going to provide the international codes, if you want the JP ones check the sources.
Beldum - Up, Right, Down, Left, X, R, L
Slowpoke - Up, Down, Right, Left, Y, R, L
Hoothoot - R, L, Y, X, Left, Right, Y, X
So if you're unable to use any of these buttons on your 3DS, you're unfortunately locked out of obtaining these Pokemon in Dream Radar.
Sources:
- Dream Radar's manual (Details controls)
- Serebii's page on Dream Radar (Lists all of the obtainable Pokemon in Dream Radar, their abilities, and both the JP and Int. codes for unlocking Beldum, Slowpoke, and Hoothoot)
- My own experience playing Pokemon Dream Radar (This isn't something I can link to so you'll just have to trust me!)
