hi,
A) wiring the RK56 mic direct to the Cobra 29 LTD Classic seems to
be no problem about it.
B) using EB-1 Astatic echo board in between the two might produce
hum if :
1) the unit ( Astatic ) is not properly shielded , meaning it should
be mounted on a metal casing, and have a proper grounding
on the case.
2) there is unregulated supply on the echo board.
3) the echo board is mounted near the large transformer of the
power supply
4) there is no proper matching between the echo board out
and the Cobra mic in.
5) the output of the echo board is not properly shielded.
here is a simple matching between the output of the echo board
and the input of the mic in Cobra 29
the in = to be connected to the echo out
the out = to be connected to Cobra mic in
the variable resistor or sometimes called the potentiometer
will match the impedance of the echo out to the mic in.
it can be any from 5 K to 10 K ohms

hope this help you, thanks for using Fixya!