I'd like to swap the speaker on an electronics kit for a reed relay
This looks straight-forward. From the receiver schematic, the "speaker" is in fact a piezo sounder and is DC driven so you can wire a relay coil in it's place. You will need to add a small general purpose diode (1N4148 or 1N914 etc) across the relay coil with the cathode connected to +V and the anode connected to the "speaker" output (T2 collector). You will need a small 9V relay with a coil resistance of at least 500 Ohms.

EDIT:- I've attached a (badly drawn) sketch ...