In our survey, we looked at dogs over the age of 3 that were exercised wearing harnesses were 2.3 times more likely to have suffered an IVDD incident than those exercised in collars. This does not imply causation; it may simply be a reflection of the fact that dogs that have previously suffered an IVDD incident may be exercised in harnesses rather than in collars.
Dogs that pulled on the lead rather than walking to heel were no more likely to have suffered IVDD, irrespective of whether or not they wore a collar or a harness.
90-95% of all Dachshund disc herniations occur in the middle to lower back, not in the neck. It, therefore, seems unlikely that walking a Dachshund in a collar increases its risk of back problems.
If your Dachshund has had an IVDD incident with one of the cervical (neck) discs, ask your vet whether it would be more appropriate to use a harness than a collar, for walking your dog.