First, before I get into how to completely disable the mousepad, including its left and right click buttons, on any laptop let me restate my opinion: DON'T do it!! It makes a lot more sense to mask the actual area that moves the mouse with a thin piece of cardboard (e.g., the back of a notepad or single or doubled over index card) so that the mouse pointer cannot be moved but you have access to the actual left and right click buttons, which are far more reliable when those are called for than any screen reader's emulation is. At least if those are hard buttons, the mousepads that use a thin area at the bottom left and right sides that act like those buttons when touched are problematic.
One should always check the mousepad/touchpad controls in Control Panel. In the case of the laptop I'm using, an HP 15 series, that item is Synaptics TouchPad, to determine whether your touchpad supports toggling it on/off as part of its own controls. I cannot possibly say where these would be located across brands. It requires looking at the settings to find it. Some do, some don't. In the case of many Synaptics TouchPads, there is a setting under Tapping Settings entitled, TouchPad Disable Zone Settings which, if turned on via its checkbox, makes a double tap at the top left corner of the TouchPad toggle it on or off. If that checkbox is checked, a secondary set of radio buttons with the grouping entitled, Top Left Action, becomes accessible, with the two radio button choices then being Switch TouchPad off for one session or Switch TouchPad off. I have to believe "session" in this context means "until restarted" while the just plain off will stay off, even after reboot, unless one were to intentionally double tap the upper left corner of the TouchPad.
In addition, if I open Mouse Properties from Control Panel, many laptops have a checkbox available to Disable internal pointing device when external USB pointing device is attached. I've seen many people use this, with the dongle for a keyboard-mouse combo, to use the external keyboard but also disable the mousepad at the same time whether the wireless mouse is actually powered on or not. I've also seen people use this and just attach a USB mouse, then placed "out of the way" as a way to temporarily disable the TouchPad, but such that a mouse for someone sighted is available or that it can be unplugged to allow an assistant access to the mousepad.
Now, after all of the above, you can use Device Manager to disable a mousepad/touchpad, and it will remain off between boots on most systems until you use Device Manager to enable it again:
1. Open Device Manager
2. Expand the Mice and other pointing devices entry. Under which you should find your touchpad. In my case, that is Synaptics SMBus TouchPad.
3. Select your TouchPad device.
4. Bring up the context menu and see if you have a Disable option. Mine does not, because it can be disabled by its own control software. I have seen some that are able to be disabled. If you've got a disable option, activate it. It should now stay disabled until and unless you were to repeat this process and choose Enable from the same context menu.
I personally prefer either masking the touchpad or using the option to disable it when an external pointing device is connected. It's way easier to reverse.
By the way, if you're worried about the external mouse possibly being bumped or moved, it's a simple matter to make what I call "a hobbled mouse" or "a treated mouse" where you tape over the laser port on the bottom which is what detects movement over a surface. When that's taped over, the mouse will not recognize that it's being moved, but the left and right click buttons (and scroll wheel, if it has one) remain available for use.
Brian - Windows 10 Pro, 64-Bit, Version 20H2, Build 19042
Always remember others may hate you but those who hate you don't win unless you hate them. And then you destroy yourself.
~ Richard M. Nixon