Your factory restore will most likely only restore to a drive of equal or larger size than the original (the OEM restore process is an image expansion, so if the image is of a 500 GB drive, then you'll need at least 500 GB for it to work). If you have a Windows install disc from the same generation as the CoA sticker, then you can do a fresh install to the new/smaller SSD with the code on the sticker. But note that this WILL NOT move over your preferences/settings/etc from the old HDD without additional effort.
All that said, have you considered a hybrid drive (I some manufactures are calling them HSSD or SSHD). These have a decently sized flash array smashed to a large spinning disk drive. Built in firmware determines the sectors with the most consistent IO demand and moves them into the flash portion (faster IO) and keeps lower request requirements on spinning disk where cheap is good enough. You get more size, you get more speed, and you don't have to classify what needs to be on the SSD vs HDD by hand. Thats a lot of winning.
With the hybrid design, the migration is also as simple as "clone existing drive to new drive; expand partition(s) as necessary." So things will 'just work' when you start with the new drive. And the cloning can be done with a myriad of freely available tools (including some that probably come in the box with the new drive, or probably a download link these days, who needs more CDs).