Will doing this blow my speakers?

Solid state amps are ok to do (no damage to the speakers or amp)
Tube amps I am not certain about. (I only know for certain do NOT turn on/off a tube amp with no load.. ie: no speakers, as this can blow up the amp)
And yeah, the way to find hum is to do one part at a time.
I would first disconnect all sources from per, then see if pre/amp combo hum.
If so, try just amp.
Usually a hum is a ground loop in the nest of wires... in cluding power cords and grounds.. or a bad interconnect...
The most common hum is an ungrounded TT or a poorly grounded turntable.

You're right- They were just kooks. You won't hurt anything turning on the amps w/o a signal source. If you touch the interconnect RCA plug's post, you'll get quite a buzz from the speakers though.

Use a gray 3 prong to 2 prong cheater plug on your power cords to lift the ground. If you have a AC ground loop you can use the cheater plug to find it.

One way an amp can damage a speaker is by supplying DC current, either by internal damage or a faulty soft-start circuit (the "thud" you hear when powering up). This, if it happens, is independent of downstream source components. If your amp is okay, I agree, you can safely power it up with no source components.

I don't think you need to be reminded to change connections only while every component is unplugged. Don't place faith in the power switch alone.

I had an AC hum problem in my stereo system and it ended up being the cable feed from my local TV cable provider. The fix was a filter where the cable hooked up to the digital cable box. Just thought I would mention this to you as I never considered this as a possible source.