Smaller, Faster, Cheaper to Alpha Centauri
However, I bet you could do it with a much smaller sail if you were willing to orbit the sun a few times to build up momentum before heading out of the solar system.
Or, you could accelerate them with a laser beam.
In that case, the only problem I see with using a small sail would be decelerating once you reach your destination.
And if I'm right, there's no reason why we couldn't launch an interstellar nanoprobe within a decade or less.
Here's my plan:
Launch a whole series of solar sail nanoprobes, one after the other, to Alpah Centauri.
Each probe would transmit data to the next probe that was launched behind it, eliminating the need for a transmitter powerful enough to broadcast all the way back to Earth. Low-power signals would be relayed back to Earth, using something similar to Internet protocol.
Continue doing this until you have a constant "loop" of 50 or more nanoprobes circulating between Earth and Alpha Centauri.
If Alpha Centauri proves to be "boring," you could simply re-direct all (or some) of the nanoprobes to a different star system.
If we wanted to do a sample-return mission, we could decelerate the probes with a laser beam once they returned to our solar system.
But by the time the probes returned to Earth, hobbyists would be able to retrieve them with their family space ship.