There's a couple things here to keep in mind.
Be cautious about mobile apps, especially with a custodian service (wos) or a service which can be abused easily (muun). They are likely tracking some device ID so all of that will be correlated as you go through this multiple times. I assume you're already wiping the app after each time, but that's still not enough.
The more people use non kyc custodial services in this way is going to bring them heat. You're treating them as a custodial mixer. That doesn't end well. These services are not low risk.
Timing analysis. You're leaving papertrails with your multiple on chain transactions. You should stick to purely lightning if you want to avoid chain analysis, maybe with one swap later on not near the kyc withdraw.
I'm pretty sure primage is revealed on chain when you do a swap. So that can be correlated with source or destination of payment by your lightning wallet, especially if that lightning wallet already knows all about your payments. Phoenix, wos, muum all see your destinations, amounts, and payment hashes when you spend. And this includes muun entirely since it is only on chain swaps. These will be trivial to compare to a specific on chain utxo at the end.
You just need one or two of these things to happen to break your flow. But that all depends on what you're worried about happening. Is it leaks? Private companies? A local heavily armed gang or mafia with the power to infiltrate organizations across the world? You start with the problem, not the solutions.
Tldr, too much on chain use, too much correlation with custodial use, too much lightning wallet privacy leakage. Depends on what you're trying to protect from who.
This is a great response. I think many people don't understand the logs that are collected about devices, how much entropy they reveal, and the analytics tools out there. Even these "off chain" data can be analysed at scale sometime in the future - especially if you're aiming to use some of the most popular wallets (that are more likely to have logs subpoenaed).
However, I think your point about knowing what you're protecting against is key. Even OP's setup is better than nothing - reduces chances of being confidently targeted by most actors. But if you're a journalist who is hated by your government they could turn the eye of Sauron on you and figure out a lot of the picture pretty quickly.
Excellent point about approaches like this actually turning custodial solutions like WoS into targets themselves.
I agree, I think a threat model is important here. It is all a spectrum.