I am reseaming the teak decks on my boat. Each plank has one rabbeted edge which, when laid next to the adjacent plank, leaves a 3/16"-1/4" seam to fill between the two. The rabbets started out about 1/2" deep. As the teak has worn down over the years that depth has decreased. In some spots it is as little as 1/8". I need to increase the depth of the rabbet in those spots so the new caulk has enough teak to adhere to and stay in place.
There are a couple of really bad ideas (for me at least) out there to do this. They involve a router or a circular saw. There are jigs that help with these but they are cumbersome and not something I want to use. I have used a 1/8" chisel on some spots which works but is slow. I am thinking that a small hand/rabbet plane would be the best alternative but I have no idea on what to look for. I use quite a few tools i.e. table saw, routers, drill press, power planner, etc. However, I've never owned a hand plane in my life. Any suggestions on a plane that will handle that small of a rabbet? Any comments and help appreciated!