Use the handheld.
You aren't going to be out in the fog that much but it is nice to have when you need it. I have a number of things in a Dry Bag which I attach to the Halyard bag forward of the mast. My Motor repair kit, plugs, flashlight, compass, matches, first aid kit and anything I feel would be of help. My river knife and whistle are on my PFD where I can get to them. I also keep a 75 ft throw bag in same location for MOB. I don't think a day sailer needs a mounted compass, and anywhere you would mount it would get in the way of somthing at some time you don't need it there.  Good sailing.