
Not all dachsies are prone to back problems, I have found the smooths have more of an incident than the longs or wires and research of lines and getting from a responsible breeder should reduce the risk even more.
My dachsies are not allowed to do the stairs till 6 months old and then up only and carried down till a year old, curtailing too much exercise means the muscles supporting the spine don't get a chance to strengthen, they do get on the sofa but are shown how to jump onto a bean bag and then the floor when getting down, did try steps but they were in too much of a hurry to get down.
I wouldn't trust my dachsies off lead unless the area was completely enclosed, I use an extending lead which allows them to run on ahead and back to me meaning they cover more ground than I do on a walk.
The coat on a wire hair can vary a lot, a pup who is very hairy when young will need more grooming/stripping than one which is less hairy, a friend in Australia has a litter at the moment and out of 6 pups one of each sex is hairy and the other 4 are not but still look like wires.
Good Luck with your search