Metric just doesn't fit - unless you can find a 6.35 mm wrench. They come in rounded sizes: 6 mm is really too narrow, and 7 mm doesn't get a good grip so it slips over the ridges, and will ruin the shape of the nut so you end up with no grip at all.
Wild suggestion - could we have double-standard nuts, half 1/4, half 6 mm?
The Allan wrenches have the same problem, by the way. Sometimes you find weird sizes in tool shops on the continent, like less than 1 mm, but never any standard imperial ones ....