Looks like you can get a 4TB Seagate SSHD and throw it into a USB 3 3.5" external enclosure. The drive will automatically put files into the flash portion of the drive, so all you need worry about it getting an enclosure that isn't junk.
I don't think that any company sells one already in an enclosure.
Now.....that being said. The SSD's in these drives are 8GB single NAND chips which means the bandwidth is pathetic in terms of raw speed. The NAND itself could probably muster 30-50MB/s on it's own. It's strength comes from accessing small files extremely fast. That's where you see the advantage of the SSHD. For just raw transfers to and from, these SSHD's will offer no advantage. You would be better off getting a USB enclosure that allows 2x 2.5" drives in RAID 0 (so it's still small size as you indicated). Depending on money you can get 2.5" drives in 1,2,3,4 & 5TB sizes. Might be able to must 200MB/s out of these in RAID 0.