I have been working on a feather wallet plugin to be able to simply perform xmr<->btc atomic swaps using the inbuilt feather GUI. It is very straightforward to use but I would still recommend reading this quick blog post on how atomic swaps work if you don’t know so you understand what is going on behind the scenes.
This is also only the second release so there may still be some minor bugs in it, if you find any please post an issue on the github.
I do not know the specifics of how MimbleWimble works, but like XMR, transaction history and metadata is no longer public. Your trace of coins are effectively evaporated when you move coins over MW to another wallet from your “compromised” wallet, and from there you convert to XMR/move to another LTC wallet and pay merchants who accept LTC without MW. Obviously, basic OPSEC is expected but other than that the technology is supposed to work fairly well.
You could also do a swap like LTC->XMR->LTC and spend it that way, losing some money in the process but soothing paranoia in return
If that is how it works then the best way to use it would be to keep a pool of LTC that went through MW then spend from it. You do not want to MW a specific amount then immediately move that same amount to somewhere. Because the receiving party could possibly determine the origin before the MW pass-through just based on the amount.
Yes of course, transacting amounts close to the payments you want to make is a bad idea.
I should probably study a bit more about MW, it’s been a while