I'm no EE, but have a fascination with electronics. Here is what I would recommend. You would need some current limiting device on the circuit with the razors, and some sort of current detecting mechanism with the light bulb. If the current passing through / power consumed by the lightbulb drops it engages the current limiting circuit connected to the razors. Seems like I've seen this type of thing before with op amps.
But there are probably better ways to do this.
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