Yep, you'll damage the lens and/or the body if you try to fit a J12 on a Contax IIA or IIIA. This lens is only compatible with the prewar II or III.
For a 35mm lens compatible with the IIA/IIIA, look for the postwar Zeiss Biogon, any of the Nikkor RF lenses or the recent ones offered by Cosina Voigtlander in Nikon S mount. The Nikkors or the CV lenses will probably be the cheapest option. I use a Nikkor 35/2.5 on my IIA body, and this lens is outstanding.
The difference in the Nikon and Contax mount won't be an issue with 35mm or wider lenses. With 50 or longer your focusing will be off, especially at larger apertures and close-up. Nikon made Contax-mount versions of their 85, 105 and 135mm lenses. Optically and physically identical to the Nikon mount versions, only identified by a 'C' engraved on the underside of the barrel.