I don't plan to mix KYC-ed with non-KYC, that's why I mentioned that even after proceeding (either using LN transfers+fixedfloat or Monero, as other user suggested too), I plan to leave the coins coming from Binance in a wallet totally separated from my official non-KYC coins*, because I'd still consider the outcome (from LN or Monero) "non-kyc-ish" coins. By the way, if I start moving my btc from Binance to another wallet, I'd continue with the next step only once all my btc leaves Binance and my balance there is $0. It won't be their business what I do with my money afterwards. Why a bank would freeze my money? I have never funded Binance using a bank transfer or credit/debit card. I have only used their built-in P2P, so I have traded internally with other users.
*I already started buying non-KYC btc from DEX+P2P and that btc is stored in another wallet, so, for me, these are my only official non-KYC coins.
Now I'm sure it's not a good idea to use my official non-KYC coins to provide initial funding to an LN wallet (therefore I won't mix them with the ones coming from Binance), so I'm considering the route suggested by another poster (Binance=> swap=>LN=>Wallet/HW)
I'm exploring the Monero option too, but I see that there are lots of DEX exchanges with bad reputation in reddit for scams or people losing money (at least those able to trade XMR). I have found that Tradeogre and Robosats are a bit better positioned on this matter, in case I use the Monero option.