Which shields have damaging parries?

According to this guide, the Lynel Shield, Savage Lynel Shield, and Mighty Lynel Shield are the shields that deal damage when a parry is performed

Parry Power As described in the Nintendo Guide, this is the damage you do when you perform a parry action. Only certain spiked shields like the Lynel Shield will damage the enemy when you parry.

The reason why these shields are able to deal damage is due the blades that are attached to the shield. From the Lynel Shield wikis

The shield's blades grant this shield the ability to cut when the shield is used to parry (which is normally used to initiate a Perfect Guard). Link can even cut grass by parrying with this shield in grassy areas (doing this will not reduce the shield's durability).

According to my own experience as well as this link, the only shield that does damage when using the parry "attack" is a Lynel shield. Typically most players try to avoid doing this, since the attack is extremely close range, slow, and leaves you open and vulnerable for an excessive amount of time.