Declining a paper review after accepting it and seeing the manuscript
The best course is to just inform the editor that you are unable to perform/complete the review as it is outside your area of expertise. The title led you to think otherwise. You are sorry, but others are better qualified to judge and give advice.
I don't see that as anything strange at all, and no one is likely to think less of you.
What would be wrong is to give a review of something you don't comprehend completely. No one benefits from that.
Just be honest with the editor. No one knows everything.
Having very briefly -- and foolishly -- been an editor, I wish all reviewers shared your concern of "going back on my word". Far too many not only don't deliver promised reviews, but do so passively-aggressively by just not saying or doing anything, leaving editors to chase them down.
I also wish reviewers who discover they are not qualified, or for any other reason not able, to do a review would politely back out and give information as to their reason so that the editors can redirect the paper more effectively to someone who can do a good job. Crappy, unqualified or cluelessly superficial reviews are a real problem.
With all of this in mind, I would think more rather than less of any reviewer who backs out for reasons such as you describe, thoughtfully and in a timely fashion.
As to the "access" issue, indeed authors reasonably expect their unpublished work not to be blasted out to an unknown selection of colleagues/competitors in their field. All reviewers should not let unpublished work received in confidence influence their own work. Of course, there is an unavoidable "what has been seen cannot be unseen" element, but I'd expect this be less of an issue when you have decided the paper is outside your ability to engage with in detail, and when the expectation is you should stop reading it, I'd say delete it once your refusal is a done deal, and try to forget what you have seen.
I fully agree with @Buffy's answer, but would like to a add two "middle-ground" possibilities.
I as well as some colleagues have been in a similar situation in the sense that an important part of the paper turned out to be outside our respective expertise, while the reviewer was fine with reviewing most of the paper (as they concluded from title and abstract).
In such cases, the reviewer has been telling the editor that they are fine reviewing most of the paper, but it turned out that a substantial part is about topic outside expertise and they suggest/ask permission to consult named colleague who's an expert on that topic (example: expert on the application area consults expert on statistical data analysis).
My experience is that the editors were happy with that suggestion.
I suspect that it is sometimes very hard work for editors to find particular combinations of expertise in one person (consider particular application area + particular measurement technique + data analysis/statistics all of them at a sufficient level of expertise to judge whether the authors have been working correctly).
(I've been in the position of asking to consult a colleague as well as in the position of being the colleague who was asked to provide further expertise.)
In case my level of expertise is "almost fine" for the critical topic, i.e. I only need additional expertise confirming/refuting my conclusions but I'm confident that I can extract all relevant information from the manuscript, I've been abstracting (like a minimal working example) the situation and discussed my questions with colleagues without revealing the paper. As this is like reading up the topic in literature or a textbook, the permission of the editor is not needed.