Debit card as non resident

Hi!

I have a tourist visa on 10 years with unlimited entries and I want to apply for a debit card in capital one bank but I'm looking for mastercard debit card so in my main country I won't pay the big fees like 3-4% so I see that only Capital one offers that.However I dont want to get Discover card because in my country there are many problems with them, they dont accept them nearly anywhere.

Is this possible and whats the procedure?