Are you working for screen?
Personally, I would probably draw the path in Photoshop, or perhaps use image trace in Illustrator, understanding that no smooth vector path will exactly follow any pixel edge except a true horizontal or vertical line.
But again, if you need to be working with pixels, but also need to avoid snapping to the pixel grid, switching the ruler dimensions to Points should allow you to do that with no numeric changes -- one-to-one correspondence between the units, only the name of the unit will change.
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