Ground my body to DC (USB)
Grounding mats, properly installed have a large resistor ( think 1000 kohm ) between the mat and earth ground.  The mat may take a static discharge of thousands of volts and the the resistor limits the current as it drains away the static charge.  That high impedance will not quench the AC field picked up by the body.

Grounding to USB will couple the AC field picked up by the body to the USB 5V return.  As the USB DC source is isolated from AC - there may not be a path to drain off the AC field voltage.  The AC will not go away and now the USB port will rise and fall with the picked-up AC field.

You are right to pause before wrapping bare copper around your wrist and plugging it into an outlet.  DO NOT DO IT!

In order to help with the underlying issue that is leading to grounding the body, please state what is that underlying issue.