I think a minority of laptops have soldered-on HDs. More have them hard-attached now than a few years ago (when almost none did), and many recent laptops have "mSATA" connections, which is more like a RAM connection than a cable. You could achieve the same thing with an mSATA connection as you would with unplugging a cable by removing the mSATA drive/card, and applying a thin strip of something non-conductive over the pins, and plugging it back in. Just please don't use something adhesive; the residue after a few applications/removals can screw up connectivity when you want it to work.

That said, I'd imagine there's an economies-of-scale advantage to having soldered-on drives (to say nothing of the economic benefits of un-upgradability: sorry folks, but there aren't enough people to whom part-swap upgrades are important to sway the hardware industry at large on this issue, though a few small manufacturers/lines will probably target that market). As a result, I'd imagine that we'll see more and more of them in years to come, though I'd be happy to be wrong about that.

'course, I don't recommend bringing your data into a country you consider hostile regardless of whether you've set it up so a cursory search doesn't find it. If the country really is hostile to your interests, that won't stop them if they want your info.