[Baertram]

Ok, as I said you don't need the weapon switch event anymore, because you can exchange the textures 1 time at the player activated event. After they are changed from original textures to NONE they won't show up anymore, even if you change the weapons.
And if you reload or rezone the player activated event will be fired again and replace the texturs with NONE again, so you should be fine.

Here is the result:

--Just a function to reduce redundant code
local function RemoveActionbarBorders()
    --remove borders at action buttons
    for slotNum = 3, 9 do
        local button = ZO_ActionBar_GetButton(slotNum).button
        button:SetNormalTexture("")
        button:SetPressedTexture("")
        button:SetDisabledTexture("")
    end
    --Remove the border texturs now until next ReloadUI or zone change
    RedirectTexture("/esoui/art/actionbar/ability_ultimate_framedecobg.dds", "")
    RedirectTexture("/esoui/art/actionbar/abilityinset.dds", "")
    RedirectTexture("/esoui/art/actionbar/abilityframe64_up.dds", "")
end
 
--Callback function for the player activated event (upon zone change or logging in new)
local function Callback_Player_Activated(...)
    RemoveActionbarBorders()
end
 
--Put this somewhere where your addon gets initialized, e.g. inside callback function of EVENT_ADDON_ON_LOAD or just at the bottom of your addon
--Register for the zone change/player ready event
EVENT_MANAGER:RegisterForEvent("NoActionbarBorders", EVENT_PLAYER_ACTIVATED, Callback_Player_Activated)
 
--Callback function for the addon loaded event (executes for EVERY addon that loads!)
local function Addon_Loaded(eventCode, addOnName)
--Is THIS addon HERE found?
    if(addOnName ~= "NoActionbarBorders") then
        return
    end
    --If you got here your addon is found so execute the following code lines:
    --Unregister this event again so it isn't fired again after this addon has beend loaded
    EVENT_MANAGER:UnregisterForEvent("NoActionbarBorders", EVENT_ADD_ON_LOADED)
    --Register for the zone change/player ready event
    EVENT_MANAGER:RegisterForEvent("NoActionbarBorders", EVENT_PLAYER_ACTIVATED, Callback_Player_Activated)
end
 
--Register the event ADD_ON_LOADED to get started with your addon. As this event will be called for EVERY addon you need to
--check your addon#s name inside the cllback function so it won't execute your code for EVERY addon!
EVENT_MANAGER:RegisterForEvent("NoActionbarBorders", EVENT_ADD_ON_LOADED, Addon_Loaded)

Btw: there is still one small texture line left beyond the ultimate skill