You can use XMR.to, Shapeshift.io, or Changelly.com over TOR to move funds directly into another another blockchain currency. So have fun following things around Bitcoin blockchain like some high tech sleuth, but thats a wild goose chase.
I buy all my cryptocurrencies through those kind of services nowadays, because there's no risk or temptation to keep coins on custodial exchanges, instead of in a private wallet. As well as no worries about withdrawal limits (although shapeshift has fairly low per transaction limits, just make an additional transaction)
For unlinking the transaction, the only currency you want to cross-chain into is Monero. With its Ring Signatures and Stealth Addresses it is a private blockchain by default (in comparison with some other cryptocurrencies that have a secondary optional privacy feature like Zcash/Shadowcash/Dash).
I'm actually surprised that the ransomware isn't taking Monero directly yet as some exchanges have direct Monero/USD markets already.