However, it usually doesn't matter, often small SMD carrier boards are manufactured with plated through holes that are then cut in half, to make a solderable carrier board, with
holes on the edges that are half-plated in a semi-circle now.
For a header connection on the edge, if a little bit of the pad is routed off it shouldn't matter too much. You just have to worry about the mechanical strength of the PCB.
Actually, this does matter quite a lot. Almost no manufacturer will make boards which have the risk of holes being cut open by the routing process.
Of course, it can be done, but it requires much more attention by the manufacturer to prevent the plating to be damaged or even ripped out of the hole.
And as usuall, more attention means more cost, and usually not available on simple pooling services.
As for this specific situation, use the smallest hole possible, so that would be the 0.7mm. This is finished hole size, so the actual drill will be 0.8 or so. this means the hole is 0.4mm away from the edge. If the edge is routed (instead of scored / V-cut), then this shouldn't be too much of a problem.
The folks at Pcbcart are very communicative, so just order the board and send the files. And wait for any comments, if any. Also, often it helps to ask if the issue(s) they raise are really, really a problem; Sometimes they agree the issue "shouldn't" be a significant issue for production, and simply proceed. Or maybe they'll charge a bit extra for tighter manufacturing tolerances, in this case probably because of a reduced annular ring.