I think you are correct on the short scale length of the B4ce, but the important detail is the amount of string that passes beyond the bridge saddle, which can sometimes call for a "medium scale" 32" scale set. That said, if Frono is correct and there is no more there than on your typical Fender-style bridge, then you will want the actual "short scale" set.
A piezo pickup functions off of physical vibrations, so you can use any type of string with one, provided it creates enough vibrations for the pickup to sense. The limitation of magnetic pickups is that the material of the string must have magnetic properties, so no luck if you had a pure nylon string like you find on ukuleles, ashbory basses, etc. Phosphor bronze acoustic strings would be no good on an electric instrument with a magnetic pickup, as the pickup would only sense the core of the string, resulting in a thin, subdued, and unbalanced sound.
But in your situation, you can use any bass strings you'd like, though I don't think anybody makes fully nylon strings for full-size basses, only the uke-size ones. Speaking from personal experience though, flatwound strings may sound great on an acoustic bass, but they will be quieter when playing unplugged, especially on non-jumbo acoustic basses like the B4ce. Essentially, the less depth of the body, the less low end volume (which is where flatwounds really get their power). Also, I've found heavier gauge strings are typically louder on acoustic basses, since they create more powerful vibrations that project better. With that in mind I would probably steer clear of that super light gauge rotosound set. The D'Addario Chromes should do fine, especially since they tend to produce more mid and high response than a lot of other flatwound alternatives. I would just take care not to mix up "Medium Scale" and "Medium Gauge". Buying medium scale sets when they meant to grab medium gauge or medium tension strings seems to be a common mistake players make and the likely reason for why I can often find medium scale sets in open packages at a discounted price on the Amazon Warehouse Deals site.
One of my past bands did several radio performances, but for one of them we decided to just go with our kitchen-table approach... which meant all acoustic, with me on the cheapo Ibanez acoustic bass that I really only ever used for acoustic rehearsals and/or playing by myself on the porch. I always kept chunky flatwounds on that one and in this context it worked out quite well. We just used two normal radio/vocal mics for everything that night. My two bandmates did vocals, banjo, and guitar all on one mic, standing back a bit, and I stood much closer to the other one with my acoustic bass. The result was a nice thumpy uprighty kind of sound. If you had been standing 15 feet away in the studio though, you probably would have only heard the vocals, banjo, and guitar.