If your wildshape is physically capable of having a fighting style, it should benefit, probably
A straightforward RAW reading of those two sentences, together, says, no. However, there a few confounding factors.
Blind Fighting was released with TCoE, well after the above clause from the PHB. So, it is entirely possible that the PHB rules were written without any anticipation for an edge case like Blind Fighting.
Multi-classing is complicated. As Crawford suggests, there are different ways to interpret multiclassing rules. If a DM rules that class features are to be kept strictly separate, a paladin's class may not be subject to the same restrictions of a druid's in wildshape.
Specific beats general. Wildshape is general class feature, whereas Blind Fighting is a specific class feature. Though the exact sense of "general" and "specific" aren't totally clear here.
In my personal opinion, the provisionsal
However, you can't use any of your special senses, such as darkvision,
unless your new form also has that sense.
reasonably refers to innate physical traits of the creature. Hence, wildshape's operation on them.
If a tiefling has darkvision as a function of her species, and then wildshapes into a different eyeless species, she shouldn't retain darkvision. However, if the eyeless species has a different special sense, she gains it. This implies that sense is tied to shape. But, a fighting style is not necessarily tied to shape; they only correlate ("so long as the new shape is physically capable").
A fighting style is a learned skill, usually a class feature or feat. With styles like Great Weapon Fighting, Dueling, this much is obvious. And the text corroborates this; c.f. the feat Fighting Initiate:
Your martial training has helped you develop a
particular style of fighting. As a result, you learn one Fighting
Style option of your choice from the fighter class.
A paladin, in particular, earns their fighting style at level 2.
Starting at 2nd level, you adopt a particular style...
Since the fighting style, and vicariously the sense, is acquired, it is not a function of shape so much as of skill. So, arguably, it should not necessarily suffer the consequences of changing shape.
Consider a real-world example, the echolocation (blindsight) of a bat, which is a function of it's innate physiological structure--it's shape. The blindsight of a bat is a function of its shape, whereas the blindsight of the Blind Fighting style is a function of training. So, if you want to play with a bit more fidelity to reality, you might rule that the benefits are retained.
A conservative leaning DM who is sympathetic to the "realistic" argument could still argue that the style, and vicariously the sense, is tied the the shape of the creature insofar as nuances of coordination, precision, and balance are prerequisites. So a shape that very closely approximates the
humanoidoriginal is necessary to gain some kind of blindsight.
Alternatively, a conservative DM may rule that the carried over "class features" may strictly refer to the Druid Class because they were not written with the optional multiclassing rules in mind.
Would a wildshaped druid still be able to practice the fighting style of Interception? Unarmed Fighting? Tunnel Fighting? That depends on entirely on its situational shape. So, the same should apply to Blind Fighting ...
... if the new form is physically capable of doing so
Who knows? The wording of the rules gives no further clarification on the origin of the sense. The clause
You have blindsight with a range of 10 feet.
could refer to a preternatural awareness of your surroundings, operating entirely through intellectual and/or spiritual faculties--precisely those faculties that compose the Druid's immutable mind and spirit throughout the wildshape.