Training can absolutely help with the nipping. One thing that I start with my puppies before they ever go to their new homes is rewarding "four on the floor". Since puppies usually jump up when they nip, I reward them for keeping four feet on the floor when a person approaches. If they have their four feet on the floor when I approach they get treats, pets, let out, etc. This is also part of the dog manners class I attend. When we work on greeting behaviors the rule is four feet on the ground for attention from strangers. This takes a lot of self control especially from a very excited puppy but as they learn to master this they also learn how to calmly interact with humans.
When you are doing laundry or other housework, you can keep a Champ's breakfast or lunch in a bowl nearby and click him for sitting or laying down while you do your chores. Just click and toss him his kibble where he is laying. He should pretty quickly catch on that laying down and staying calm really pays.
A more structured way of going about this would be to teach "Go to Mat". http://www.dragonflyllama.com/%20DOGS/Levels/LevelBehaviours/TL9GoToMat.html