|>>|| No. 2531
A white noise generator is a relatively simple project if you're handy with a soldering iron, and it'd wouldn't be hugely complicated to hook up to an alarm either.
I'd recommend looking for a more 'musical' noise generator that allows you to do white, pink, brown noise etc and blend them, as I suspect even for your needs pure electrical white noise might be too harsh. Something based on something like the Doepfer A-118 Noise module would be good, and I think you can get the schematics to make the circuit yourself.
As >>2530 says a much simpler solution already exists, but if you're after a project then here :