I would remove the old drive and place it in an external enclosure. Install the new SSD. Boot from the external's Recovery HD using OPTION boot:
1. Restart the computer.
2. Immediately after the chime press and hold down the
"OPTION" key.
3. Release the key when the boot manager appears.
4. Select the Recovery HD on the external drive.
5. Click on the arrow button below the icon.
Select Disk Utility from the Utilities Menu and click on the Continue button. Partition and format the SSD Mac OS Extended, Journaled. Clone the external drive to the SSD:
1. Select the destination volume from the left side list.
2. Click on the Restore tab in the DU main window.
3. Select the destination volume from the left side list and drag it
to the Destination entry field.
4. Select the source volume from the left side list and drag it to
the Source entry field.
5. Double-check you got it right, then click on the Restore button.
Destination means the new SSD. Source means the external drive.