What you will need depends partly on the radio.
If the radio will receive ONLY with the mike plugged in, you'll need a relay. That's the only way to prevent the transmit audio from frying the speaker when you release the mike.
If your radio receives the same with the mike unplugged as it does with the mike plugged in, the relay won't be necessary.
In purely generic terms, you'll need a circuit to sense that you have released the key, and a timer circuit to 'hold' the radio keyed until the noise has played.
Seems to me I have a hack around here somewhere for an old "EES" or some such sound effect that used one of the ISD sound-storage chips. That chip has an output that goes high while the stored sound is playing, and goes low at the end of the recording. That function made the timer circuit unnecessary for that one. Just used some diodes, if memory serves. Gotta go back and see if I really did write that one down. Can't remember.
But uh, the answer really is "It depends". Depends on the radio and the noise toy both.
I suppose you could "marry" a roger-beep board and a noise toy to do that. First place to start would be to draft a schematic diagram of each. You won't find that in the instruction sheet they pack with the beep, or the noise toy. Kinda hard to modify a gadget without a road map to what's already in it.
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