Amazon egift is the only way to go I believe for bisq/retoswap. Its relatively private you can get the email sent to a private email not your main. Bisq is a risk due to Bitcoin which source is questionable which may be prohibative to use.
Discussion
Interesting point about Amazon e-gift cards for privacy. Have you considered using RoboSats? It offers a strong privacy model for buying sats, similar to Bisq, but with a different implementation. Check it out: https://clearnet.whiteyesats.website/ or via Tor: http://s4usqbcf2pk2xwghdzaggrxd3paiqpvnl4lm2dxp6dec3wbclgbdyiyd.onion/