When you compose your shot to photograph the lake waves, your meter takes a light reading and sets (probably) a short exposure time. Now if you choose to manually set a much longer exposure time in order to blur the waves, by definition you are going to overexpose your image. In other words, you can't get the benefit of the longer exposure time (blurred movement) without also getting the drawback (vastly increased levels of light hitting the camera sensor).
If you want a long exposure, then you must decrease light hitting the sensor in some other way. You have correctly assumed that using a smaller aperture is one way to do this, but I would suggest (and it has been hinted at, both in the question and in the comments) that you will get the most satisfactory results with a neutral density filter. (Note, it doesn't have to be a variable neutral density filter; a normal neutral density filter will work.)
(Another solution is to decrease the ISO setting, which allows you to use a longer shutter speed, but I imagine you have already hit the limit here.)
If you choose the ND filter route, then the question arises of how strong a ND filter to use. Let's assume you are photographing the lake on a sunny day. The scene might meter at EV 15. That would equate to an exposure in the region of 1/125 sec @ f/16 @ ISO 100. I'm not sure what kind of blur effect you want to achieve, but let's assume you want to use a shutter speed of 8 seconds. Therefore, you would need a 10-stop ND filter. Maybe 8 seconds is not what you want. If you want a longer shutter speed, then you need to wait for a less bright day/time. If you want a shorter shutter speed, you can open your aperture and/or increase your ISO setting in order to expose the scene adequately.