To answer your specific question? If you plugged the Switch into the USB Type C port on your PC all it's going to do is charge. That has nothing to with the Switch itself and everything to do with the port on your computer. So if you want to do it that way you're going to need a capture card.
But that's not what you necessarily want. What you're asking for is a way to put the video output of the Switch to your monitor while having the sound go somewhere else. And that's a different question entirely. Because there's a fairly high chance that if you plug a set of headphones into the headphone port on the Switch it'll send audio over that rather than HDMI. It also has bluetooth so, in theory, it could support bluetooth audio devices. But we won't know for sure until it's actually in people's hands to test it out.
