Supplementing aguijonazo's answer,
You can refer to the following 大辞泉 entry. Grammatically, a natural way to interpret the sentence is that there is omitted part, as suggested in the answer. A practical way to understand it would be the usage expresses the feeling of surprise, similarly to its usage as 終助詞.
のに
[接助]《準体助詞「の」+接続助詞「に」から》活用語の連体形に付く。内容的に対立する二つ��事柄を、意外・不服の気持ちを込めてつなげる意を表す。「東京は晴れな―大阪は雨だ」「十分言い聞かせた―理解していない」「九月だという―真夏の暑さだ」
「それはまあ、よく忙しい―、気をつけておくれだ」〈人・娘節用・後〉
[終助]《の文末用法から》活用語の連体形に付く。不平・不満・恨み・非難などの気持ちを表す。「これで幸せになれると思った―」「いいかげんにすればいい―」
For comparison, a reasonable situation to use 足場が[/も]ないのでよじ登れんよ would be when the speaker goes ahead of Luke and reaches the pole first, then reports to Luke that it is not climbable.