Although that breed of dog might adapt to being alone much of the time, there are some things you need to do.
1. Do not get a puppy: You are not going to be around enough to socialize and play with a young puppy. A bored puppy is more likely to get into problems with chewing, digging, and excessive barking.
2. Get your dog a companion: Dogs are social animals. Since your dog is going to be alone so much, it is important that he have another pet to spend time with. I am not sure of your situation but adopting or rescuing a second adult Chihuahua is a good idea.
Chihuahuas do shed, but since they are small, it is not as bad as with a large dog. They also bark, but if you exercise your dogs when you are home, make sure they have toys, and of course, leave them together so that they are not isolated, the barking is usually not excessive.