what's everyone using for non-custodial swaps these days?
A lot can be checked here and they've got reputation and experiences for each thread you'd see.
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https://bitcointalk.org/index.php?board=223.0changelly through ledger live most of the time, changenow if the rate's better
These swaps aren't recommended and I will discourage you from doing any swap directly from your Ledger straight to these exchanges which might require to sign the transaction.
Apart from that, if you still own a Ledger then you better find another hardware wallet e.g Trezor models.