You'd do better to do a fresh install on the SSD, move all the files you would like to keep off the HDD to some other media, Format the HDD, and replace the files on to the HDD.
The only real alternative I've seen is the use of Paragon's software, which extracts the OS files from the HDD and then allows you to put them on the SSD. I have seen this used at an office that was migrating quite a few PC's and there wasn't any issues there. Although if I were you I wouldn't see the benefit in paying the 20 or so quid it costs.