So your computer is encrypted, yes? Generally, and I think I am representative of the community on this forum, when I say, we do not advise the use of Apple's encryption option, unless you are a spy or engaged in industrial espionage of some sort. It really is unnecessary if you take reasonable precautions to protect your data. On the other hand it can complicate the retrieval of data in the case of file corruption or breakdown of your device.
Of course it is entirely up to you.
I take it from your answer that erasing the Seagate drive would not pose a problem. In that case I would be inclined to use Disk Utility to Erase, Name and format the drive to Mac OS Extended (Journalled) and perform a full backup using the Apple Native Time Machine app. This will take some tine dependant on the amount of storage on your computer and offer you the option to encrypt your backup (if you must) see;
http://kb.mit.edu/confluence/displa...ime+Machine+backup+drives+on+OS+X+10.9+and+up
My personal choice though would be to unencrypte the Mac HD then create a Bootable clone.
This has a few advantages over the Time Machine backup in that it can boot if your HD crashes and run just like your internal HD until repairs can be made. Also it's format is easily read on any Mac .