I'll be surprised if at least Shotaro's actor doesn't return to do Double's voice. It shouldn't take too long. In the worst case scenario, they might also go with Ganbaride voice clips. Those apparently were pre-licensed to be reused everywhere already, considering how they've been reused in multiple games, unlike the tv show recordings.
Of course, that's assuming that Double's role is rather small and they can get away with him using just cathphrases and some generic words to the other two Riders, but, if his role is actually significant, then they'll probably either need one of the original actors or use a sound-alike (athough hopefully they can get closer to Shotaro's voice than they did in the Let's Go Kamen Riders Net Movie).