With regard to square waves vs sine waves, is it not mathematically prudent to use sine waves instead of square waves in some cases due to modulation issues or possible frequency band limitation issues?

I am not well-versed in the mathematitics of calculating two 19kHz audio channel signals which are to be transformed into covering a frequency around 38kHz.
However, one source describes how to generate left and right channel outputs 90 degrees phase shifted signals, using two leds in parallel, which will cover the 38kHz pulses by ways of both positive and negative "difference" pulses. Others talk about phase shifting one channel by 180 degrees to allow for higher voltage to drive the LEDs.

What is your take on a effective way of combining two lower frequency "audio" channels to cover higher frequency pulses?

As for putting my smartphone in harm's way, in this day and age I think that everybody has leftover smartphones which have been made redundant by planned obsolecense. Fortunately, some of these devices have a chance to be made useful again. I like the idea of repurposing leftover hardware.