That is a good idea. But instead of carrying multiple types of thread, why not just some fishing line that would work with almost any colour. Just have to get the dull looking type (for lack of a better description and proper model names). Don't want the shiny stuff.

And probably to add to this would be replacement shoe laces (not paracord as it probably wouldn't fit the holes in a dress shoes - not to mention it would stand out and formal events are all about being visually conservative). I did this when I was living on the road for a few years as a contractor. Shoe laces (no matter what they are made out of) would fail at the wrong time.