Communication - 2 Battery Powered Circuits, 1 Conductor, no common ground
There will be a vague capacitive connection between any two separated bodies.  The capacitance of this connection will vary with a lot of factors, including surface area, distance, humidity, phase of the Moon, the price of tea in China, etc.  It's really not possible to predict even within an order of magnitude what the capacitance will be on any given day.

On the other hand, if two people P and Q are holding swords X and Y which are not touching, it's very likely that--because people's bodies have a much larger surface area than their swords, capacitor PQ will be large relative to PY and QX, which will be large relative to XY.  For an AC voltage on PX to appear on QY, current would have to pass through small capacitor XY, which is very small, and some of that current would uselessly return through capacitor QX.  On the other hand, if the swords touch, then the current would only have to go through the much larger capacitor PQ.

While one would have to do some experiments to determine the optimal coupling for signal generators and signal detection circuitry (my recommendation would probably be to use a single-frequency sine-wave generator in each suit, along with some LC-resonant tank circuits, so that each input circuit would be blind to its own generator, and maximally sensitive to the other).  I would expect that with swords are touching, the strength of the coupled signal would be enormously higher than when they are not.

Note, btw, that higher frequencies will almost certainly work better than lower frequencies, though if you go too high (over about 100KHz I think) you'll start having to worry about being regarded as an "intentional radiator".