I've googled for this and haven't really gotten any sensible hits?
In my experience it's really pretty non-critical what you use for this; back in the day I hacked together a speaker by using one of a pair of amplified Walkman speakers. (The speakers in question each had their own set of 4AA batteries and were connected to the Walkman by a Y-cable that had a stereo 3.5mm plug on the walkman side and mono 3.5mm plugs on the speakers. This meant the TRS-80's cassette out could just be plugged directly into them; the "hacking" part was I wired a volume knob I salvaged from somewhere between the amp board and the speaker because otherwise it was *waaaaay* to loud. Granted it was probably pretty dumb to put the resistor on the output of the amp instead of the input, but, eh, it worked.) More recently I've gotten sound out of my Model I by:
A: Hooking it up to one of those dumb disco-ball party speakers:
View attachment 1254319
B: Plugging it into the front-panel Mic input on my desktop computer, starting up Audacity, and turning on the recording monitor so it plays the Mic input out the speakers.
(The latter method is what I'm using to CSAVE programs instead of actually using a cassette deck, to load them I of course hook the cassette input to the headphone output.)
Unfortunately all the amplified PC speakers I have lying around have captive cords so I can't connect a set up to the TRS-80 without either a gender changer or making a cable, but I can't think of a good reason why there would be any problem at all using them. Do you still get this mysterious hum if you *don't* have the Cassette deck hooked up at the same time as the speakers via your Y cable? I can't say I ever tried having a cassette deck and a speaker hooked up at the same time, I've always just swapped the cable.