You can always buy a channel using ecash from a channel provider to your node... Have a VPN and/or run the node over tor. You will have no outbound liquidity then but that's OK. Then you can send a utxo or liquid to boltz then the boltz swap can 'pay' your lightning channel you bought/rented with the ecash.

Then just close the channel... The utxo from that what I understand has zero connection to you, you were using a VPN and now you have a random utxo that doesn't leak your IP or identity beyond the minimum.

Or at least that's my understanding but I am not an expert it depends on your exact situation