You need an old cable converter box or a VCR that can tune into cable TV channels. The cable box or VCR will be able to receive channel 95 or 96 and it will output a signal on VHF channel 3 that your old TV will be able to pick up.
This works. I just hooked up my famicom to a tv that doesn't have channels 95-97. Run the NES Rf switch from the famicom to the VCR. Run av cables from the VCR to the Tv. Set the channel to 96 on the VCR, set the famicom to game and channel 2 (or famicom channel 1 and VCR at channel 95), and make sure you have switched the tv to whatever input you have the av cables in. You should be good to go.