Problem with your proposal: The possible interpretation is too broad. Nobody knows which currency you mean when using "~". This means you could use "~" when describing any (abstract) form of money, but not a specific currency.
That said, I also think that "BTC" and the "B-with-legs"-symbol are already too widespread to be abolished as currency descriptors of Bitcoin.
ya.ya.yo!
Agree, too much possible interpretation. 10B would be better than 10~ : P