Install a external hdd in a Ps4

So I recently bought a external 1TB HDD. I planned to take the disc out of it's case and pop it in the Ps4. Will it work to make a backup of the ps4 on the external disc, then disassemble it, and then install it in the Ps4, or must I do the whole backup and restore process like when you get a new internal hdd? I bought a external instead of a internal hdd, because it was much cheaper.