Wakeup PC upon mouse click but not mouse move

It would be a cool feature to have, but unfortunately it does not appear to be possible; Windows can be configured (via the powercfg command -- powercfg /? for more detail) to treat input from a given USB HID device as a reason (or not a reason) to wake from sleep, but not to differentiate between types of input. Writing a program to do that sort of differentiation would be relatively trivial, but by the time the machine can run that program to decide whether or not to wake up, it's already awake, and would instead have to decide whether or not to go back to sleep -- which probably doesn't help.

As a workaround, you might consider simply disabling the mouse as a device that can wake the PC; if you don't have a keyboard on the table next to the mouse, then this may not be a useful option, but it looks to be as close as you're going to get to what you're looking to accomplish. To do so, open a command shell and run

powercfg /devicequery wake_armed

You'll see your mouse device named in the list, possibly along with other devices. To disable wake input from the mouse, do

powercfg /devicedisablewake <name of mouse device>

And if you decide to re-enable it later, do so via

powercfg /deviceenablewake <name of mouse device>

Or you could just switch off the wireless mouse when you're not using it, which as a bonus may make its battery last a little bit longer.

When trying to disable my mouse from waking up my computer entirely, I stumbled upon a solution. Windows might differentiate between your mouse movement sensor and the buttons.

My mouse movement sensor is under the Mice and other pointing devices section of Device Manager as HID-compliant mouse.

My mouse buttons are under Keyboards / HID Keyboard Device.

If I disable the ability for the mouse movement sensor to wake my computer, but leave the buttons (under keyboards), it will do exactly what you want.