if you give access to ETH before receiving the BTC, the user can scam you,
To avoid this, an intermediary program is needed, which will unfreeze access to ETH only after BTC is received.The issue is that neither chain's contracts can access the other chain's contracts. So any system that requires 'monitoring the other chain' won't work. Hence the commitment-style implementation that Submarine Swaps use is so far the best idea that I came across for swaps across chains.
The ETH smart contract cannot observe the BTC blockchain.
I understand. Thank you for reminding me of this. 
In my idea, networks BTC and ETH do not intersect in any way. Iintermediary program, which, just does not allow one of the parties (mixer and user) to scam, connects ETH and BTC networks (conditionally), checks the receipt of the required amount to the addresses, controls the fulfillment of the conditions. Maybe have a look into those.
There's also a video presentation by Alex Bosworth. Not sure if it's good, though.
It is possible and if so, then I apologize that I wasted your time with "inventing the wheel". There's also a video presentation by Alex Bosworth. Not sure if it's good, though.
I don't know anything about submarine swap or and first saw the term in your post, but I'll look through your links and try to learn more about it. [/quote]
No need to apologize! I'm really interested in this topic and glad to discuss. If you've got more thoughts on submarine swaps or other, maybe better ideas for these cross-chain swaps and using them for mixing, keep the discussion going!