A CW Key is apparently a switch used for transmitting Morse code. Make sure to click through to the individual pages to see them in use, e.g. https://www.youtube.com/watch?v=ghx3r_OFmt4
Trying to think of another activity where one hand is doing something so complex while the rest of the body practically looks bored. Nothing comes to mind.
Another note: since in the US there are only four letters allowed as the first letter (A, K, N, or W) and will be 4-6 characters with further restrictions on which can be letters and which can be numbers (2-by-3 being the most common, 1-by-2 and 2-by-1 only being available to higher license classes, where those are the numbers of letters before and after the region identifying number). You could use this in your detective story, along with other details like inferring where they got their license from or getting more details from the FCC. Following this up with an inspection of the radio and which frequency was recently used, could make for some interesting detective work. Ham Radio doesn't make very many appearances as a plot device.