Then my advice to you will be the same thing I've been doing as a tutor for years now with my screen reader users who have a laptop: Mask off the mouse touchpad part of the mousepad as a whole, leaving only the hard left click and right click buttons exposed. You then have access to these when you need them, without need of emulation of any kind, and you do not have issues with mouse pointer movement.
A piece of cardboard that's about the weight that is used on the back of small notepads, blister packs that you get all sorts of stuff in, or even cutting the corner off of an old greeting card such that you retain both layers gives you enough thickness to prevent mouse movement.
I always suggest taping down the left side like it's the spine of a book while taping down the right side with a tab that allows it to be lifted easily in the event you have a sighted assistant for anything, as the vast majority will be incapable of doing anything without the ability to move the mouse pointer somehow for point and click. You just flip it shut and tap that tape tab back down when they're done and you're good to go.
If you happen to have a newer laptop where the edges of the mouse pointer touchpad are not well defined, you may need a sighted assistant to get the right size mask cut and affixed. If it's one of the conventional laptops where the mousepad size can be clearly felt around the edges of the bezel in which it sits, it's generally something that's DIY whether you have any vision or not.
Brian - Windows 10 Pro, 64-Bit, Version 20H2, Build 19042
The depths of denial one can be pushed to by outside forces of disapproval can make you not even recognize yourself to yourself.
~ Brian Vogel