How can I switch my mouse between two PCs without using software?

You should look into mice that have built-in KVM capabilities. For instance, the Logitech MX Vertical can connect to four different devices, so you can easily switch without much hassle!

The Logitech MK850 combo is great for switching between devices. It has the capability to connect via Bluetooth and also supports multiple dongles. Just a heads up, there might be a slight delay if the devices go idle.

If you've got a Razer mouse, some models have a nifty little switch on the bottom that lets you toggle between different connection types. Mine has USB-C, 2.4 GHz, and Bluetooth options, so I connect it via Bluetooth to my laptop while keeping the dongle plugged into my desktop. Just keep in mind it's not exactly seamless, but it works well for switching between machines.

You can definitely use a physical USB switch to flip between two PCs. It's a simple solution that avoids any software issues.

I recommend checking out a cheap KVM switch if you want to manage multiple PCs. Also, Logitech mice like the MX Master can connect to multiple devices and switch with a button on the bottom, which is pretty handy!