On many mirrorless cameras the shutter is open by default (even when the camera is closed), so not even one shutter "count" on this type of usage (the shutter is only used when taking a photo, and not even then if in silent mode is used). Shutter lifespans are in the tens of thousands to hundred of thousands normally. It's good to know the value when buying used (because you don't know what you are buying, some cameras have such a high burst rate that you can reach hundred of thousands in hours if you keep the button pressed).

For many cameras you can find a power line adapter that replaces the actual battery and connects to power (Canon cameras cannot charge their batteries in-camera so this is a must for them).