You cancel them get new cards and then use gift cards or prepaid visa / etc cards. Sorry if that wasn't clear.
You don't use a "real" visa card on any online account.
For amazon I wait til I have around 500 dollars worth of stuff to buy then get prepaid cards then if or WHEN the account gets hacked you are only going to lose what ever is left over and never give access to your bank account with debt card to anyone.
WHY? you might ask.
I had my bank account attacked 3 times and my credit cards attacked 2 times and one time they locked up my all my money for 3 months until it was resolved. So I had to call my parents for the first time in 20 years to borrow money to pay rent. I had 100k+ in saving tied up.
Another time I was working in China I had to pay all my rent and bills 3 months before leaving so I didn't access my accounts over VPN and have them shut down again.
One of these times because I was accessing my account over VPN through the UK to the USA to pay my power bill I got my bank account locked up / shut down so when I came back I had to open another account just to get my money transferred over.
Just to make the point of how fucked up banks are this was Wells Fargo who was later charged with closing down accounts for any excuse because they employees were getting fees and pushed to open new accounts so they were caught closing down accounts for any reason just to make this quota this was coming from the top. I know they fired some people but after that I moved all my money two different banks US Bank and Citi-Bank.
At this point after all this bullshit I pay in cash for everything I can and use cash to buy these limited pre paid cards to avoid all the hacking. Everyday you see another company exposing data or getting hacked so I try to protect myself.
Like do I trust that New Egg has a good security people? Sure. Do I trust that New Egg or anyone has billions of dollars in security coders fighting all the people out hacking and stealing money. No.
Maybe I am just unlucky.