Have a bone on the second armature which has copy rotation/location of a bone in the first.
Place the two bones so they have 100% influence on the two halfs of the seam and it should keep the edges welded together.
Other than that I think you may be out of luck, it’s tres difficult/ beacoup impossible to control the vert positions of a rigged mesh.
This will sound like a Workaround, but it isn’t really… well, Kind of… but not really…
… but wouldn’t it be better you actually used one Mesh for the visible Dude and the separated Meshes doing the actual Motion are actually invisible Cubes (or just using one Armature)? Even if you manage that the Vertices are like merged at Runtime, the Shading will still have a Seam.
I’ve done it and it works well.
Here’s a blend file example: human_male_base4.blend (966 KB)
And here’s how the effect looks:
You can see that the arms move independently of the legs, he can crouch, walk and even lay down (in a later version of the character I did this) and meanwhile the arms can be posed for shooting or a relaxed pose and you can even have another bone for the torso for aiming and torso twisting.