A whole new Nutcracker is not exactly what Boston Ballet was hoping to mount this holiday season. But when the city’s Wang Center booted its longtime December tenant in favor of a touring show with better special effects, the company was forced to reinvent its holiday staple in a new space, with less room to maneuver, smaller audiences, and a smaller budget to match. The result will be a Nutcracker that Boston audiences won’t recognize: “About 40 costumes have been redesigned… The company is using, for the first time, an extensive network of computer-programmed sets of moving and LED lights for a different look,” and new scenery aims to make the best use of the space.