The animation is setup is to get close to 1:1 representation of your hand/finger positions. The way you can do this with a skeletal mesh is that you IK to the elbow/wrist position which the leap motion estimates, and then you use the orientations of everything else which will put the fingers in the correct form without distortion. The fingers might not match your real finger length but the relation of the fingers in the mesh will line up correctly for nearly any type of skeletal mesh hand.
If you wish to use this animation setup, then the correct way of updating the position from an external source is to update the Anim body which the animation blueprint uses.
AnimHand has a convenience function written in C++ which grabs the information directly from a leap hand (leap-ue4/AnimHand.h at master · getnamo/leap-ue4 · GitHub) and this is called in blueprint (in leap connector I believe). What you need to do is to set the Anim body data similarly to leap-ue4/AnimHand.cpp at master · getnamo/leap-ue4 · GitHub (this can be done in blueprint), all the setting functions are publically accessible. Another way would be if you could serialize the leaphand data and pipe that over the network, but that might be a bit harder to do.
Optionally setup your own skeletal mesh animation rig which uses raw data you pipe in a different way.
Finally a last option is to fix the blueprints to work correctly in UE’s networking system through replication, which is something [MENTION=425607]Joris Vial[/MENTION] seems to be working through.