Currently, the guidance for UKM applications does contain wording that reflects the outcome of the Romein case. "
https://www.supremecourt.uk/cases/uksc-2016-0165.html" . The basic premise being that specific rights were afforded to men that weren't afforded to women. This included the ability to register a child as a British citizen in some cases. The result of the courts' decision being that it is impossible to determine which mothers were "actually'" impacted by this discrimination, and officials must therefore grant citizenship to those who fall under this category. This is an oversimplified explanation, but you seem like if given the appropriate breadcrumbs, you'll have no trouble following the trail.
I am no expert on this, and truly can only speak from my experience, but your wife's circumstances sound very similar to the above case. With the exception of your wife being born in a commonwealth country.
Also, I agree with Secret_Simon, There is no cost apart from the ceremony fee of £80. As long as the information in your application is correct and (I have to say it) truthful, there is very little risk. The only real cost is the time spent acquiring the appropriate documents and the ceremony fee.