Haha! I'd never thought of using the "Cool S" drawing for the sats symbol before. Honestly, I kinda like it because it is so recognizable and would be immediately acceptable in wider culture.

We technically don't have a unicode for sats yet, so I'm open to suggestions. In the past, I've used "≑," "≡," or "≣" as a compromise. We can also use 1μ₿ = 100≑ (or "uB") like we do for $1 = 100¢. Then, intelligent keyboard apps or word processors can automatically replace "uB" with "μ₿," or maybe a new glyph like the attached.

https://protos.com/bitcoin-satoshi-symbol-stacking-sats-design-community/