Sechel, you can be honest; is that the only teshuva from rav moshe that you know of, because it contains words sent to the Lubavitcher rebbe? I won’t judge you for it, it’s not your fault, it’s nust your background which leads to such things. Like the anti kollel people who basically know one line of rambam.
Rav moshe’s shaving heter was intentionally oral; he had reasons for not wanting to write about it. That doesn’t mean he didn’t explain it; he did, and the reasons were very convincing. Some yeshivishe guys don’t use electric shavers, rather they use haircut machines or trimmers, which don’t have sharp blades and leave a tiny bit behind. That’s what more than half of my friends did in my bochurishe days.