If I have WBTC on ETH network, then I use ~ to swap WBTC from Ethereum network to BTC network, is the swap info, btc destination address and/or other info stored in any database or even in the main ETH network?
Same question can be done in a BTCB to BTC swap info with ~ bridge.
BTC and ETH (WBTC) are not anonymous chains, so you don't get anything as anonymity. And you gave as choices a shady platform (risk to lose money) and a centralized exchange (make everything even less anonymous). No.
If you want to do it right, the options you have are either a proper mixer or coinjoin, either atomic swap with Monero (which although I've read it's live, I'd give it some more time before using it).