**かべがわ** is the only correct reading in your context.

へきそく is a rare reading used in medical contexts to translate *[parietal pleura][1]* (壁側胸膜【へきそくきょうまく】), [*parietal peritoneum*][2] (壁側腹膜【へきそくふくまく】) and so on, but laypeople do not know this reading. (BTW, *parietal lobe* of the brain is 頭頂葉【とうちょうよう】.)

I don't know when to read it as かべぎわ. Since the old orthography is used, it may be some obsolete reading. かべぎわ is usually written as [壁際][3].


  [1]: https://en.wikipedia.org/wiki/Pulmonary_pleurae
  [2]: https://en.wikipedia.org/wiki/Peritoneum#Layers
  [3]: https://jisho.org/word/%E5%A3%81%E9%9A%9B