Non-fermented vinegar substitute for Dijon mustard
Another allergy sufferer claims you can swap in pure vitamin C &amp; water for the vinegar.  It wouldn't be Dijon mustard, which strongly depends on the flavor of white wine, but it could be a strong, fine-grained mustard.

If the flavor isn't quite right, you can also experiment with citric acid crystals (sour salt), or a mix.  For a bit more wine flavor, consider adding a small amount of white grape juice.  Saba (concentrated unfermented grape must) would be even better, although it's difficult to find in some countries.