When I tune using my FT-840, I put it in AM, reduce output power to a minimum, and press the "MOX" button to get a continuous carrier.
Try it with CW, MOX (TUNE) and reduced power. Less bandwidth and same effect.
In the absence of any modulation, there will be no bandwidth difference between AM and CW. I guess I always put it in AM out of habit, though you are correct, CW would be the one to use.