You should be able to write an Eclipse plug-in to give you a one-button solution, if you wanted it that way.
However, if your project is properly set up, simply doing a re-build would trigger a hot-deploy of the updated webapp.
Hot deployment doesn't always work, and during the days of the dreaded PermGen storage, you tended to only get 2 or 3 before you ran out of RAM, but a full stop/rebuild/deploy/start isn't always necessary.