You won't damage the light meter by accessing the shutter. To really get at the shutter blades you will have to remove both the front and rear lens elements. The rear elements come out easily as a group, you'll see two sets of notches for your spanner, use then outer notches. The front element group is more tricky, usually only the retaining ring for the front element will come off, leaving the rest of the lens group in place. There is a second set of notches for a lens spanner, but they are hard to get to without a special tool. The front retaining ring is made of aluminum, and is easily damaged, so be careful.

My experience with getting shutter blades clean on Canonets has been hit and miss. Sometimes cleaning them helps, sometimes it doesn't. They needn't appear oily to stick, and shutter blades which appear to have oil on them may work fine. If the shutter mechanism itself needs cleaning, you had best send your camera to an experienced tech, it is a more complicated job.