Do you run SSD + HDD?
Last time I installed Steam, I just put it on the HDD. This way, I don't have to think about reinstalling Steam and all it's games next time I format my OS by leaving the HDD as it is.
I don't think you can just move the Steam folder to another device. I think the installed games makes certain entries in the Windows Registry. You could move all the games over though, and move them back after reformatting. That might work, so you don't have to download major parts of the game? I'm not sure, but it's worth a try if you can't just move it all.