Can I use Cursed Shovel to discard cards from my opponent's deck if they have Bibarel with "Reassuring Dam" Ability on their Bench?
Yes, since Cursed Shovel is a Tool card and not an attack, Ability, Item card, or Supporter card its effect would not be blocked.
Source: TPCi Rules Team (2024-03-21)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH2_157
SWSH2_157
SWSH105_60
SWSH105_60