Hardwiring radar detector

Yes it can be done.
First, before cutting off the plug make sure you know which wire goes to the center of the plug and which wire goes to the edge of the plug. The center will be connected to +12 volts (wired to one leg of a fuse in fuse block with an inline fuse holder before going to fuse with the fuse from the cigarette lighter plug in it) and the edge wire will go to a ground (wire should have a terminal put on the end of it and using a screw attach to a metal part of car; floor pan). The +12 v wire I usually strip the end off, twist, and then wrap once around one leg of the fuse and stick it back in. Remember only one leg or you will be bypassing the fuse and defeat its purpose. You need to decide if you want the detector on all the time or just when the ignition is on, it makes a difference which fuse you choose. I usually like a fuse that can be done without temporarily, like horn, cruise, etc just in case it does blow. The use of solderless terminals make the job easier with a pair of crimpers and must have electrical tape. Be sure also not to have the +12 wire in a position that may get cut into or come in contact with metal, it will short and blow the fuse.
The same thing can be done with hardwiring neon and most any +12 volt accessory.
I chose not to cut off my plug, but to buy an extension plug for an accessory and hardwire it. This way my plug is always there if I want to unplug and move it to another car. There are also multi-plug accessory outlets (3-4 outlets) that might be helpful if you plan on more in the future.
Good Luck