Look at their channels and open to one of their partners with a lot of capacity, then swap away
Can't you swap straight from LN wallet to btc onchain address without opening channels? From let's say Primal wallet?
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How did you get so many sats into primal?
The implication is you can buy KYC from your exchange, open a channel, then swap to no KYC
If your exchange supports lightning then yes it will also work
