Yes—expect heavy, obvious mechanical vignetting, especially at 10mm. The Sigma 10-20mm is an ultra-wide lens, so it sees a very wide angle of view; putting a much smaller 67mm opening in front of an 82mm filter thread is a large restriction.

The small APS-C size difference doesn’t really save you here. The Canon vs Nikon APS-C difference is only about 5%, while stepping down from 82mm to 67mm reduces the opening by about 20%. That mismatch is far more significant than any extra image circle margin.

In practice, an 82mm-to-67mm step-down ring on this lens is likely to cause severe, objectionable corner darkening at the wide end, and possibly throughout much of the zoom range. For an ultra-wide like this, it’s best to use filters sized for the lens, or larger filters with an appropriate step-up system rather than stepping down.