Perhaps you could do it with Bitcoin Core. On the sending wallet's node, create a raw transaction with a fee of 0 using createrawtransaction and signrawtransactionwithkey. Enter the transaction on both the sending and receiving wallet nodes using sendrawtransaction so that they both see it. I assume the transaction will be added to the mempools and will not be relayed because the fee is too low.

I have never tried it, so I don't know if it will work.