Changing Nintendo email because I lost the old one

So today I went to go swap my Nintendo email (currently logged into my switch) and wanted to swap it to an email I have. I talked to customer support, and apparently the only way they could confirm that this was me was by asking for my bank details on a purchase I’ve made. Now I’ve never made a purchase through a card on my Nintendo, so nobody could help me (2 agents asked the same question btw). So now I’m stuck and need to swap my email, what should I do and is there anyone that can help.