Not at all, it will work fine (and I have done it often).
Some logic/reasons and explanations -
The wattage of a device (talking about electronics here, and ignoring stupid extremes like shorting two wires) is the maximum it can draw. The voltage is fixed, and it is the current that varies. Thus you can use a device which consumes less power without issues.
3.5" hard drives are typically used in desktops because they are bigger, and because they have a bigger surface area they are able to hold more data. Right now, the biggest 2.5" drives commonly available are about 1.5tb, while 4tb drives are available in the 3.5" form factor.
3.5" drives also give a performance advantage in some cases (because the outer edge of the disk is spinning faster data located here, large blocks are quicker to read).
SSD drives are pretty much uniformly 2.5" or smaller, and when mounted in a desktop are put into a bracket. SSD's, btw, use a lot less power then hard disks.
BTW, the power output supplied by the pc is 5/12 VOLT DC (not 5/12 watt, and not AC). A USB device is 5 volt, so it is possible a wall supply used to drive an external hard drive is 5 volts, 12 Watts - again, DC. This is not really relevant to making things work though.