You said "double wall alloy rim". So you're considering replacing just the rim using the old spokes? Some people would say you shouldn't reuse spokes. I've done it a few times with no problems. Mostly with quality stainless (DT and Wheelsmith) spokes, but I've also reused fairly crappy carbon steel spokes - no problems yet.
Of course, to do a rear wheel you'll also need a tool to remove the sprocket, and a spoke wrench. Most importantly, if you're reusing spokes you need to get a new rim with the correct dimensions. The "effective rim diameter" (ERD) is what counts. Google it and you'll find plenty of sites that explain more than you ever wanted to know about lacing wheels.