Can you use a Disarm, Shove or Grapple as your OA? I see no restrictions against it. Am I missing something?
The key here is whether the "special attack" requires the attack action or just a melee or weapon attack. An opportunity attack is a melee attack. It is not an attack action. Therefore, special attacks which require an attack action cannot replace it, whereas special attacks which require only a melee attack can.
No for Grapple and Shove
From Sage Advice:
Grappling/shoving are part of the Attack action (PH, 195). Take the Ready action to grapple/shove outside your turn.
Yes for Disarming Attack (the fighter maneuver)
When you hit a creature with a weapon attack, you can expend one superiority die to attempt to disarm the target. (PHB 74)
you use your reaction to make one melee attack against the provoking creature. (PHB 195)
A melee attack typically uses a handheld weapon (ibid)
I think that it's fairly clear that an opportunity attack is a weapon attack, and can therefore become a disarming attack if the fighter expends a superiority die.
Yes for the Optional Disarm Rule (note that there is no disarm rule in the PHB)
A creature can use a weapon attack to knock a weapon or other item from a target's grasp. (DMG 271)
As above, it only requires a weapon attack, not an attack action. However, you will need to ask your DM (if you are not the DM) as to whether they are using this optional rule.
Yes, no and no.
A Disarming Attack requires a Battlemaster manoeuvre and a weapon attack that hits so the Opportunity attack qualifies.
Grapple says "... use the Attack action ..." and Shoving says "Using the Attack action ..."; an opportunity attack uses your reaction, not your action and specifically not an Attack action.