**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】.) There are [several similar terms][3] that end with そく, all of which are almost never used outside medical contexts:

| Word | Ordinary reading | Medical term |
| - | - | - |
| 頭側 | あたまがわ | とうそく (cranial/superior) |
| 尾側 | - | びそく (caudal/inferior) |
| 右側 | みぎがわ | うそく (right) |
| 左側 | ひだりがわ | さそく (left) |
| 同側 | - | どうそく (ispilateral) |
| 対側 | - | たいそく (contralateral) |
| 腹側 | はらがわ | ふくそく (ventral/anterior) |
| 背側 | - | はいそく (dorsal/posterior) |
| 口側 | くちがわ | こうそく (oral) |
| 肛側 | - | こうそく (anal) |

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][4].


  [1]: https://en.wikipedia.org/wiki/Pulmonary_pleurae
  [2]: https://en.wikipedia.org/wiki/Peritoneum#Layers
  [3]: https://ja.wikipedia.org/wiki/%E8%A7%A3%E5%89%96%E5%AD%A6%E3%81%AB%E3%81%8A%E3%81%91%E3%82%8B%E6%96%B9%E5%90%91%E3%81%AE%E8%A1%A8%E7%8F%BE
  [4]: https://jisho.org/word/%E5%A3%81%E9%9A%9B