This doesn't appear to be how WannaCry works: as ridiculous as it sounds, it looks like WannaCry actually generates a private key on the infected machine. If you look in search_primes.cpp (from line 251) in the linked repo, you'll see that the tool is literally searching the memory for prime numbers that divide the public modulus.
EDIT: CiPHPerCoder appears to have figured how the key management works.
Right, I see that now. Adding an additional layer of RSA and per-file keys is an interesting twist. Generating a public/private key pair instead of a symmetric key seems to let them encrypt as many files as they want without keeping the private key in memory (which they relied on Windows to erase).
EDIT: CiPHPerCoder appears to have figured how the key management works.