how do i switch the mouse button for this script?

Instead of using .Activated, you can use 'UserInputService'.

local tool = script.Parent.Parent --your tool
local toolActive = false
local damage = 15
local duration = 2
local damagedChars = {}
local UIS = game:GetService('UserInputService')
local equipped = false

local function checkIfDamaged(x)
    for index, value in pairs(damagedChars) do
        if value == x then return true end
    end
    return false
end

local function onTouched(hit)
    if not toolActive then do return end end
    local Humanoid = hit.Parent:FindFirstChildOfClass("Humanoid")
    if Humanoid and not checkIfDamaged(Humanoid.Parent.Name) then
        Humanoid:TakeDamage(damage)
        table.insert(damagedChars, Humanoid.Parent.Name)
    end
end

local function onKey(Input)
    if not equipped then do return end end
    if not Input.UserInputType == Enum.UserInputType.MouseButton2 then do return end end
    if toolActive then do return end end
    toolActive = true; wait(duration); toolActive = false
    damagedChars = {}
end

local function equip()
    equipped = true
end

local function unequip()
    equipped = false
end

script.Parent.Touched:Connect(onTouched)
UIS.InputBegan:Connect(onKey)
tool.Equipped:Connect(equip)
tool.Unequipped:Connect(unequip)