をおいて（ほかに）～ないNo one or nothing else
This construction says that no one or nothing other than the named candidate can fill a particular role or meet a particular standard. It makes a strong claim of exclusive suitability: “none other than” or “there is no other.”
What the pattern actually claims
The noun before をおいて is presented as the only candidate able to satisfy the role named elsewhere in the sentence. That role should be clear: the only actor for a part, the only institution capable of leading a project, the only suitable time, or the only realistic method.
A uniquely qualified person
この難役を任せられる俳優は、彼をおいてほかにいない。
There is no actor other than him who could be entrusted with this demanding role.
AnalyzeInstitutions, times, and methods
The exclusive candidate does not have to be a person. The same pattern can single out an institution, a moment, a place, a method, or an idea.
この大規模調査を主導できる機関は、国立研究所をおいてほかにない。
No institution other than the National Research Institute can lead this large-scale study.
Analyze計画を抜本的に見直す機会は、今をおいてほかにない。
There will be no better opportunity than now to overhaul the plan.
Analyze限られた予算で全地域を調査するには、この方法をおいてほかに現実的な手段はない。
With a limited budget, there is no realistic way other than this method to survey the entire region.
AnalyzeForemost in a group versus the only candidate
をおいてほかに～ない excludes every alternative. By contrast, きっての ranks someone or something among the foremost members of a group, but does not claim that no rival exists.
彼は当代きってのピアニストだ。
He is one of the foremost pianists of our time.
AnalyzeThis is a high ranking, not a claim that he is the only possible pianist.
More examples
この交渉をまとめられる人物は、経験豊富な佐藤さんをおいてほかにいない。
There is no one other than the experienced Ms. Sato who can bring these negotiations to a conclusion.
Analyze地域文化を世界に紹介する場として、この祭典をおいてほかにない。
There is no better venue than this festival for introducing the region's culture to the world.
Analyze信頼を取り戻す道は、調査結果をすべて公表することをおいてほかにない。
There is no way to regain trust other than publishing all the investigation results.
Analyzeこの作品を味わうなら、静かな冬の夜をおいてほかにふさわしい時はない。
There is no more fitting time to appreciate this work than a quiet winter night.
Analyzeこの失敗の責任を負うべき人物は、最終判断を下した部長をおいてほかにいない。
No one other than the department head who made the final decision should bear responsibility for this failure.
AnalyzeHere the unique-candidate claim is an accusation rather than praise.