If you new oven has a white wire it is a 120/240 device not a 240 only device. There should be a label on the oven that confirms this.
I have bad news for you, you cannot use the existing wiring. The 3 wire method they describe requires 2 hots and an insulated neutral. You have 2 hots and a bare ground. The cable needs to be replaced with a 3 wire (plus bare ground) cable. The wire size depends on the amps the new oven requires.
I have bad news for you, you cannot use the existing wiring. The 3 wire method they describe requires 2 hots and an insulated neutral. You have 2 hots and a bare ground. The cable needs to be replaced with a 3 wire (plus bare ground) cable. The wire size depends on the amps the new oven requires.