[Baertram]

In chat try this script:

/script CompanionUltimateButton:SetHidden(true)

If this works add the line without the /script in front of it to any of your addons callback function of EVENT_PLAYER_ACTIVATED (if given).
If not add this to any of your addons:

local function hideCompanionUltimate()
  local ultiButtonCompanion = CompanionUltimateButton
  if ultiButtonCompanion ~=nil and not ultiButtonCompanion:IsHidden() then
    ultiButtonCompanion:SetHidden(true)
  end
end
EVENT_MANAGER:RegisterForEvent("nameOfTheAddonYouHaveAddedTheEVentToHere", EVENT_PLAYER_ACTIVATED, function(event, isFirst) 
   hideCompanionUltimate() 
end)

I have added this to FCOCompanion soon as it also needs to update the visibility after a weapon pair/bar switch e.g.
It will flicker shortly after a weapon pair switch but that shouldn't be an issue, hopefully.