How to clone existing Filevault encrypted HD to SSD with a linux live cd/usb

I have a 13-inch, Mid 2012 MacBook pro which comes with a 500 GB sata hard drive. I'm running 10.9.5 Mavericks. Of the 500 GB I have about 77 GB used whereas the rest of it is free space, this drive is encrypted with Filevault.

I have recently bought myself a 256 GB SSD from Amazon that I got for a good Cyber Monday deal, I want to clone this drive onto my new drive. I don't have a connector for the SSD drive to plug it in via a USB port and I'm wondering if I can do without one.

I have an external 2 TB hard drive, I'm thinking if I can boot my mac off a linux USB, I should be able to clone the existing hard drive with something like dd as a raw file on my external hard drive, then trim the raw image to remove the empty blocks, then start the mac with the SSD plugged in, flash the SSD with the raw image and then resize the partition so that all of the 256 GB of the SSD are available.

To me this sounds like a solid plan and I should be able to google around and figure out the commands to do all of this, I however have one concern around Filevault - will I be able to trim the partition after creating a clone on the external hard drive. I don't know if this part is possible.

Can someone confirm if this is possible, if not please suggest how you would do something like this.