I did the exact thing you describe. Unfortunately, for most software you'll need to do a re-install because, as you correctly surmise, there are registry settings. There is some good news, however. I used MKLINK at the command prompt to create folder links to many of the data locations on my old drive (now E:). I logged off of my "normal" account and logged in as Administrator. Then, for many of the folders (including Favorites, Links, Documents, Desktop, and quite a few in AppData) I created directory links to the folders on the E: drive.
For example, to get your old Documents back without having to copy anything, you'd open an elevated command prompt, change to C:\Users\YourUserName, check that there's nothing in the "new" Documents folder, then:
mklink /j Documents E:\Users\YourUserName\Documents
I did this for a few dozen folders and things just came back. It took a bit of looking around but I was very happy with the result. Just doing a few in the Users folder can save a lot of copying. You can do this for certain software programs as well. Reinstall, then delete the folder on the SSD and create a link to the folder on E:. This way, programs that keep settings and other information in the install directory (Notepad++ is one of these) also just come back like before.
I should note that while I have a 250 GB SSD for my system drive, I resolved to keep only installed software on it, no data. The system boots fast and programs load fast and my data is separate from the OS. Of course, once you're up and running, you'll probably want to spend time cleaning up the old "Program Files" folders.
Finally, I do regular backups of my system to an external 2TB hard disk through a USB 3.0 interface. I do both file and image backups. I've just learned (to my shagrin) that Windows does not back up the USERNT.DAT file with a file backup, and then when creating an image backup with more than one drive, the single image contains both drives. The implication is that if you should want to restore only the SSD image, you can't if the backup contains both drives. Lesson learned, going forward I'll do image backups of only the SSD.