Another picture of the wilting

That's a shame. Typical of cane borer damage; the larva chews a ring around the cane just under the surface, everything above the ring wilts. Other varieties of caneberry nearby can remain unaffected.

Cut and destroy the affected shoots just below the wilt. If there are any leaf nodes below that point, the cane might still grow, the branches will be smaller than the original cane but can produce berries next year.

It is probably getting late in the season for blackcaps to put up any more new shoots.

Do a search on control of cane borers and better luck next year. I have had up to 50% canes wilted, but none this year.

"It is probably getting late in the season for blackcaps to put up any more new shoots. "

Well maybe where you live, i have some still dormant in zone 6a. The guy here is in 4!
Man I won't be able to grow them if they quit before they even start!

Primocane emergence is not a lengthy process, and those pictured above were well on their way. More sprouts are possible there, but I would not rely completely on more sprouts for next year's berries by complete removal of the damaged canes.

The beetle that causes that damage certainly went right to work; my canes are usually knee to waist high before getting attacked.