Is it possible to change the black cursor texture with scripts?

This only appears to happen upon hovering over GuiButton objects. And unfortunately, there is no way to prevent this.

But there is a way around it.

You could use a TextLabel, along with the Button1Down event, and check if the mouse is within the bounds of the GuiObject in order to simulate the MouseButton1Down event.

This would look like this;

local plr = game.Players.LocalPlayer;
local mouse = plr:GetMouse();
local gui = script.Parent;
local xBounds,yBounds = gui.AbsoluteSize.X,gui.AbsoluteSize.Y;
local xPos,yPos = gui.AbsolutePosition.X,gui.AbsolutePosition.Y;

mouse.Button1Down:Connect(function()
    local x,y = mouse.X,mouse.Y;
    local leftui,rightui = xPos-xBounds,xPos+xBounds;
    local upui,downui = yPos+yBounds,yPos-yBounds;
    if (x < rightui and x > leftui) and (y < upui and y > downui) then
        print("MouseButton1Down");
    end
end)

Essentially, you can get the bounds of the GuiObject by adding/subtracting the AbsoluteSize by the AbsolutePosition.

So, left side of the ui would be: AbsolutePosition.X - AbsoluteSize.X and the right side would be the same, but you add the AbsoluteSize rather than subtracting it. Same goes for the Y bounds.

Hope I helped! And happy developing!