Well as you have a USB stick larger than the SSD, here's what I'd do
a) Download the latest Redo Backup & Restore ISO image from here:http://sourceforge.net/projects/redobackup/
and place it on your desktop
b) Install syslinux:
sudo apt-get install syslinux
c) Make the ISO image an isohybrid image:
d) Burn the ISO image to the 16GB USB stick, by (In Peppermint 6) right-clicking the redobackup-livecd-1.0.4.iso file and selecting "Make bootable USB stick" .. then pointing it at the 16GB stick.
e) boot to the 16GB stick .. once booted, also inert the 32GB stick and use Redo to create a full disk image of the SSD saved onto the 32GB stick.
f) swap out the SSD
g) boot back to the 16GB stick and use Redo to restore the backup you wrote to the 32GB stick to the new SSD
h) If necessary (though IIRC you can tell redo to do this on the fly) .. boot to the Peppermint 6 LiveUSB and use GPArted to resize the partitions on the 64GB SSD
did that make sense ?