Any of you who can offer helpful advice/experience on this? Is the loudspeaker the determining factor or will the signal itself be too crappy to do anything about?
Here are the issues in a nutshell:
a) What you have presented is a specific solution to a specific issue. There are inexpensive microphones available in the US$3- $10 range that will do just fine at voice frequencies. https://images-na.ssl-images-amazon.com ... L1200_.jpg
is one of them - Amazon.
b) if you build the tiny transmitter you have in mind and add a jack instead of a crystal microphone as show, you have the ability reduce flanking noise when you transmit. And, if you really do want to go 'high-end' and spend US$40 or so, you could go with a throat microphone.
c) One issue not addressed in the video is how to adjust the transmitting frequency overall - that is done by spreading the windings on the coil a bit, or compressing them a bit. It is unlikely that the trimmer will cover the entire 87.9 - 108 range without additional adjustments to the coil - just an FYI. Radio Locator will give you open frequencies in your area so you do not violate Part 15 regulations - and, for the record, DO take them seriously!
d) Which leads to the 'delicacy' issue. You will want to put the transmitter into some sort of project box so that the coil does not get bumped, crushed or damaged in use. Any such impact will change the transmitting frequency instantly.
Now, apart from all that - if all this is for is the purpose you describe, it will be fully adequate towards making a credible "Talking Sword". As the unit will transmit in mono, to, very likely, a mono tuner/receiver, there will be no carrier issues and as only voice frequencies are contemplated, even a very narrow spectrum will be fine. And I would suggest you not spend another nickel than you must. The worst that could happen is that you learn something about how these beasts work.
On the other hand, if you want to have a more useful transmitter, one that covers a much greater range with complete reliability and perhaps in stereo, you will have to spend much more serious money for something that is both reliable and well made. I restore old radios and vintage audio equipment, so I keep a "proper" (for my needs) FM stereo transmitter that covers my house and allows me to annoy the neighbors - should they choose to be annoyed - and still remain fully Part-15 compliant. But that unit did cost me well over US$200 as a *kit*.
Good luck with it!