I would think that, even if it were technically allowed because it is 'sort of' a weapon, I would qualify it as a 'heavy' weapon (i.e.: not light) which would disallow Weapon Finesse anyway.
There is already a way to use Dex in (defensive) grappling: Escape Artist.
Okay, but why only use it for defence? As I see it, grappling, if considered a weapon, can be "light" for this purpose. It really depends on how you picture it. You can see it as wrestling or judo: one relies more on force, the other on agility. For a monk who is all martial-artsy, I'd have no problem allowing him to use Dex for grappling, provided he has weapon finesse.
I would think that, even if it were technically allowed because it is 'sort of' a weapon, I would qualify it as a 'heavy' weapon (i.e.: not light) which would disallow Weapon Finesse anyway.
There is already a way to use Dex in (defensive) grappling: Escape Artist.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.