Hands-on skills are staging a comeback at leading-edge districts, driven by high college costs and demand for more career choices.. In America’s most surprising cutting-edge classes, students pursue hands-on work with wood, metals and machinery, getting a jump on lucrative old-school careers. School districts around the U.S. are spending tens of millions of dollars to expand and revamp high-school shop classes for the 21st century. They are betting on the future of manual skills overlooked in the digital age, offering vocational-education classes that school officials say give students a broader view of career prospects with or without college. With higher-education...