Can you suggest some ways to keep my new minature dachsund from whining and yelp...
Dogs bark to communicate they are bored, to express fear or alarm, to get attention or just for fun. In young puppies, it could also be a sign of your pet adjusting to being alone. Some puppies will out grow the whining as they age however, other puppies will need training to curb this behavior. To control excessive barking, it's important to first understand what is prompting your dogs to bark, that is, what they are trying to communicate.
If your dogs are whining between barks, it may be a sign that they are frightened or that they don’t want you to leave the house. Dogs that bark for long periods of time, with brief pauses between identical-sounding woofs, may be bored. An exuberant bark, however, usually means your dog is eager to play. If your dogs are barking only when outside, it may be that they are asking to come in – usually because they want attention.
If the barking is from boredom, preventing your dog from becoming bored is the best solution. This is obviously a lot easier said than done! First, make sure the dogs are getting enough exercise; a really good walk or playing fetch may help to tire out your dogs and prevent boredom. I cannot stress enough the importance of regular exercise. Ensure that your dogs have plenty of toys that are appropriate to their size and chewing habits – hard rubber toys stuffed with treats seem to be quite entertaining (ex. Kong brand toys).
If your dogs like to bark for joy and can't seem to control themselves, teaching your dogs basic commands to quiet and settle down may be very helpful. An additional solution can be teaching your dog to grab a ball or Frisbee when he's over stimulated -- a toy in his mouth makes it difficult to bark.
Pet Training classes will help determine what may be causing your dogs to bark and how to effectively discourage the behavior. As you stated, shock collars are not the best treatment if they can be avoided. You can also find many training tips on PetSmart.com.