Was the old Famicom switchbox an automatic? In other words, did you have to reach back behind the TV set to slide a switch on the box to change it from TV to Game? It sounds that it's the kind you will need.
The Famicom I own has an automatic switch box (a weird Japanese one that I don't use). Both the SG-1000 and Mark III came with an Atari-style switchbox (manual w/ slide switch).