But would it be traced, the funds that got onto the new address, so to speak?
Frankolala did not answer your question correctly. Read what I posted above which is the answer that supposed to be given. Your coins can be traced on the blockchain unless you use some means to block the trace. Coinjoin is the best while mixers are also good. No KYC exchanges can also be helpful.
What do you mean that I didn't give the right answer to the OP. The OP didn't mention if coins can be traced or not. He only asked if the new wallet with his bitcoin wouldn't reflect on the blockchain. If you like use any coinjoin service or mixer, your transaction cannot be traced but your bitcoin in your new wallet will be in the blockchain.
You only answered fikrett which was not part of the OP.