Simple routing question

 I have a rectangular cutting board that I would like to route a juice groove in, which I wwant to be rectangular as well but with very tight radius corners.... I have the appropriate bit, but I'm not sure how to do this.   I could make a rectangular template that I would clamp on to the board (or double stick tape it) that would sit on the inside edge of the juice groove all the way around, and then follow that around with th bit baring flush against the template.  But what if I slip -- a good chance around the tight corners -- that ruins the board.... There must be a better way to do this, but I can't seem to figure it out.... Any help would be appreciated.m thanks.