I've been playing with speedo drive gears, worms & pinions for the last week, trying to find what I need for my Mk2, so here's the heads up - the following can be done with the box in the car if necessary.
Tap gently on the end of the speedo gear shaft with a nylon hammer or something soft, and that metal cup will pop out without damaging anything. If you've damaged it, Burtons in the UK sell new ones as well as the speedo pinion gears.
Next, use a screwdriver to push the speedo pinion gear right out.The next step is to check the number of teeth on the worm gear that is pressed onto the output shaft - you can see it down inside the hole where the speedo pinion was - using a rag, wipe the oil off the start of one of the teeth and mark it with a texta or paint marker pen. Rotate the output shaft by hand with the gearlever in neutral, and count the teeth on the worm - yes, you can see down the hole but it is much easier with the box out of the car. You should have either a 6 tooth or 7 tooth worm gear - 7 is the most common by far, although I've recently heard of 8T but never seen one. If it's 7T chances are that you won't have to change it.
Wipe the end of the plastic speedo pinion gear that you pulled out earlier, the end opposite the cable, down inside the groove and you should see some Part Numbers and the number of teeth - ie 24T
The combinations are as follows from the factory:
3.54 Diff - 7T Worm - 23T Pinion
3.77 Diff - 7T Worm - 24T Pinion
3.77 Diff - 7T Worm - 25T Pinion (different tyre size - parts book not clear)
3.89 Diff - 7T Worm - 25T Pinion
4.125 Diff - 6T Worm - 23T Pinion
The most abundant seem to be the 7T - 24T combos as used in 3.77 Diff 1600 Sedans, so the odds are stacked in your favor that you likely won't have to pull the whole box apart to change that worm gear.
If your diff is original it should be 3.54 for a 2.0 Litre according to the Factory workshop manual.