I think on the current one it's m.2, not even the older full-size mSATA. When the Caron 4 comes out soon, it may be be PCIe only, no SATA (some of the new Dells are, for example.)

The X250 is the smallest that takes a 2.5" drive (although it may require a 5mm one, which are a pain.) The T450s takes a 7mm 2.5" drive, which is still a low-profile form factor, but it's a pretty common one unlike 5mm.

The 12" Thinkpad Yoga is around the same size as the X250 but tops out at 4gb memory .... It takes a 2.5" drive, but probably 5mm.

The Thinkpad 11e takes a real drive, but it's not really any less bulky than the X250; it's only real merit is being a good bit cheaper than other Thinkpad models, and it's slow as f___.

If you're willing to look at non-Thinkpad Lenovo models, the one other model worth looking at is the U31. Light, 13" screen, takes a hard drive (no idea how many mm thick.)

What's your use case with swapping the drives?