I?d go with the diode solution over relays. Suspect relay closure very noisy and would potentially create spikes on opening and closing. How much and whether it would cause a problem for the inputs on the avionics input is pure speculation. Pulling a diode to ground would be much cleaner electrically with faster transition time, etc. That said the fact you can simple connect those inputs to a mechanical switch per the manufacturers recommendations suggests the inputs are pretty robust intolerance of a momentary amount of noise on the input line. They are, as previously suggested, just detecting a threshold change. Normal ope state is ?pulled up? to some voltage level (5 volts?) and when pulled low to ground the internal logic circuitry detects this change of state when the input goes below a certain threshold voltage (what level is truly ground anyway?).
The diodes provide isolation of one input from another so that if one piece of avionics is powered down it won?t have a chance to affect the other box which, the Garmin rep alludes was possible as found during their internal testing. Easy to whip up a temporary circuit with a push button switch, two diodes, and some alligator clips. Connect the boxes and test the function. Diodes could likely be easily installed inline in the permanent wiring to the switch in question soldered in place and covered with shrink wrap for protection and mechanical stabilization.
Solid state diode good. Mechanical relay bad.
My two cents worth what you paid for it.