Unfortunately, the best answer to your question is that, there is no single word or phrase for the kind of person defined by this idiom, which includes the kind of stereotypical behavior you describe. This is possibly due to cultural differences in what is expected of women, and partly due to the fact that it represents a kind of sexist pejorative commonly frowned on.
Which isn't to sat that this stereotype or the motivations for the behavior are unknown. Far from it. Both women and men who expect to get married, but who have reached a certain age without doing so, may adopt any number of compensatory behaviors to make up for their disappointment. What is different is the relatively young age at which a woman can be called a "dried fish" in Japan, and the way the woman's behaviors contrast with what is expected from Japanese women.
But before I dive into a discussion of that, let's go over some terms that have been traditionally used for unmarried women past a "certain age":
spinster, maiden aunt, old maid, bachelor woman, independent woman, "her own woman", "confirmed bachelorette", career woman,
and various others. Note the exact value of this "certain age" varies considerably. One person or group might consider a woman of, say, 29 to be well past marrying age, while another would consider her to be in her prime.
In any case, none of these terms presumes the kind of despondent behavior you describe in your question. Someone you might call a "maiden aunt", for example, may dote on her sibling's children and display a high degree of motivation to cook for them, buy them presents, and take care of her own appearance in order to look nice when she visits them. An "independent woman" may choose to focus entirely on her career, and spend a lot of effort and money on her appearance if she feels it necessary for her success (or simply enjoys doing so).
Moreover it can be awkward to use any of these terms based on what can be considered a "traditional women's role", in modern society that tries not to impose these kind of restrictions. For example consider the highly lauded Megan Rapinoe, the 34-year old, openly gay, currently unmarried, co-captain of the world champion U.S. Women's Soccer team. In almost any context, calling her something like a "spinster" would be taken as an offensive slur against her gender, her age, and her sexual orientation, as well as a deprecation of her choice to be a professional athlete.
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I couldn't say what terms the Japanese might use to describe Rapinoe, and whether those terms would be offensive if translated, but my point is that it's difficult to move an idiom like "dried fish woman" outside of its roots in Japanese culture. The best you can do is to describe the woman's age and marital status separately from her behavior, and then use qualifiers like "it seems" or "from her perspective" to mitigate any possible offense. For example (incorporating Ben's answer):
She feels like she's an old maid who is never going to get married, and so nowadays can't be bothered to make an effort to maintain appearances.
Again you might wish for a simple answer to the question, but all of those (including most of the previous answers) would be inaccurate. Moreover the idiom itself is highly derogatory, and should be used very carefully in order to avoid causing unwanted offense.
(Edit) Let me address the one objection to this answer -- the only one I can address, since the other downvotes didn't come with the courtesy of an explanation.
To start off, there can be little argument that the direct translation of the idiom into English is highly derogatory. The only question is whether there is some mitigating factor when used in Japanese that makes it less offensive. In the comments, Mitsuko suggests:
the term is originally negative, but some woman call themselves in this way, with the message being, "it is my lifestyle and I am happy with it"
It's not uncommon to find people who are resigned to a particular lifestyle, and who choose to make the most of it. Nevertheless the kinds of behavior described as characteristic of "dried fish women" belie any sense of joy. I have to assume that "happy" means something more along the lines of, "I can't complain". The women aren't using 干物女 as a point of pride, but rather as a defensive rejection of the assumption that their lives are somehow incomplete -- even as they act in a way that makes it seem their lives aren't as fulfilling as they could be.
Alternately, a woman might call herself a 干物女 in the same way she might call herself an "old maid", but this is ironic self-deprecation, not redefinition.
So I remain unconvinced that the term is anything but a negative slur against "older" Japanese women. It might come across as mild scorn in Japan, but over here there's really no way to soften the impact. You might think something like "independent woman" is a happy medium, but not when the subtext is "old maid".
Now, it would be different if Japanese women did things like proudly wear t-shirts with 干物女 printed on the front as defiance of stereotype and custom, in the same way women in the U.S. wear shirts saying "Nasty Woman" in defiance of Donald Trump. If that's the case, I'm willing to revise my answer.
