To some degree, I not fully grasping what you're trying to achieve. That said, yes, the ANC isn't the greatest compared to Sony or Bose. It does work enough and doesn't alter the sound that much, which is something many ANC headphones do when the ANC is on.
Unless you have an iPhone which a USB C, you're going to need an adapter to use the DAC. That said, kind of defeats the purpose of that headphone in being travel friendly. They're primarily for BT. The other modes are about convenience and being robust.
If you're doing mind wires, sounds like you may be more interested in a bluetootch dongle/amp/dac such as the FiiO BTR5/BTR7/BT15 or similar device. Then you get get some closed backs with a good fit or some IEMs with a tigh seal or with custom ear molds. The latter will have a better ANC on average, and even better with custom ear molds. It can be near dead silent.