I have two copies of a Belgian 45 RPM single that are both rather clicky even after being washed. The pops occur throughout, stochastically, but occupy a small fraction of the overall time, such that the two copies together aren't missing any of the song. Having recorded the audio from each, I can imagine manually switching back and forth between them at 1/1000 speed to avoid all the clicks. What automated algorithm or method can produce a good recording from these sources?

EDIT: I will accept an explanation of why this is impossible as answer to this question.