Is the electrical buzz that is preceding the thermostat/cooling system kicking in a sign that a component is about to die or that I'm at risk of an electical fire?

Where exactly is the noise coming from? The thermostat or the cooler?

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If the thermostat, try removing the faceplate. Does it have one of those mercury switches (little glob of mercury in a glass tube) that completes the electrical circuit?

I’ve seen where electricity can arc from one of the circuit nodes to the blob of mercury as the ambient temperature approaches the trigger point on the thermostat… which causes a slight buzzing sound for a few seconds as the electricity sizzles the air. It’s all inside the glass of the mercury switch, so it should be perfectly safe.

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If the noise is coming from the outside evaporator, then you might have a failing fan switch. There are usually 2 or 3 backup fail safes in play as it’s A Very Bad Thing for the system to run without that fan. You’ll probably want to get a pro to check it out.

I haven’t looked that precisely, but I’ll check. Thanks, bro-man-du.

Slight correction… I may have overstated the “Very Bad Thing” part… which really applies more to central refrigerated air conditioning systems.

If you’re using an evaporative cooler, installation and maintenance is supposed to be much simpler… where even fan replacement can be done by the mechanically inclined home owner.