I'd suggest getting one of those baby monitors designed to be placed next to the kiddo's crib and the speaker in the other room with Mom. If I'm not mistaken, they run on 115volts A/C via a 12volt DC transformer. Dump the transformer and plug 'er in.
To wire your
radar alarm, which is not designed as a turn it on and go to sleep system as that is unsafe, you'll need to measure the amount of current the
radar's alarm speaker is getting and then wire in a relay rated for that current on it's actuation side. The other side of the relay can have 12volt DC current wired through it going to your klaxon.