If you need a physical card it needs to be mailed to you.
But on the other hand the mailed me a card to a hotel in Vietnam after a bank machine ate my card. Their virtual card works with most on-line transactions.
You can open a bank account without your spouse knowing about it. You may have to take precautions to ensure said spouse doesn't find out. I.e. through seeing letters addressed to you arrive at your marital home.
The bank will ask you how much money you are planning to have on it and the source of that. Prepare an answer.
Above is all fine.
Hiding the money and not declaring it as wealth is not. But of course you can do it and perhaps never get caught. Depends on amounts etc - at some point the Swiss authority asked us where some money was as according to them things did not add up from one year to the next. So you are entering illegal waters - you may have good reasons, but still illegal.