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)
Disarming Attack:
When you hit a creature with a weapon attack, you can expend one superiority die to attempt to disarm the target. (PHB 74)
Opportunity Attack:
you use your reaction to make one melee attack against the provoking creature. (PHB 195)
Melee Attacks
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 PHBthere is no disarm rule in the PHB)
Disarm Contest:
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.
