They obviously have accounts with the major exchanges.
However, I wouldn't doubt that they probably have their own hot wallet and cold wallets for each of the coins to facilitate these exchanges so quickly, and also to avoid the counterparty risk of using exchanges. In regards to how much they actually hold in their own reserves, you would have to ask the services themselves.
You can try Changenow, which do not require KYC up to 11 BTC, as far as I know. I use exchangers because it is much easier and reduces the risk. Any exchange, even Binance, can be hacked, or they can block an account, as Bittrex does sometimes. In both cases, the funds will be lost, so exchanges without registration are more secure.
There was a case recently where Changenow asked Bitblender to submit ID even though they were advertised as "anonymous". For that simple reason, I will not be using them regardless of what their current promises are, nor would I blindly believe anything put out there right now by any exchanger because government policy is completely out of their control.