Compared to other dog breeds, dachshunds are moderate to light shredders.
All dogs shed fur as new fur grows, and dachshunds are no different.
Wire dachshunds do not shed and require plucking (it’s painless for a proper wire) of loose hairs.
Smooth dachshunds do not grow a seasonal coat, so tend to shed less than longhairs.
There are two varieties of long-haired dachshunds: the true English creams, with luscious, full coats like a golden retriever because they are bred exclusively from long coats to long coats.
The more typical version of a long coat you will see has a shorter body coat, with long hair primarily on the tail and ears. This is the result of breeding a long coat to a smooth.
While I have never owned a silky/soft wire, I can only imagine that they would tend to shed the most with their thick, unruly coats.
Read more about Dachshund Coat Types