"I think we need to be careful about describing units as large or small"
I don't think so. Until you can produce a complete set of Planck constants compared to which we may rigorously classify ours as absolutely small medium or large, everything we measure will necessarily be numerically compared to whatever arbitrary units we ended up using owing to practical scales of our existence.
And the example you provide is a particularly unfair one given that the speed of light seems to be the largest of all possible speeds we need to concern ourselves with - most other things we measure don't really seem to have limits like this. Nonetheless, rest assured that if we ever discover some clever way to get from A to B faster than light (probably without actually needing to exceed the speed of light), "c" will indeed be considered laughably small whenever discussed in the context of interstellar travel...