Meh. sure thats possible but that level of overthinking the worrys of the road mean staying home would be a better idea. Honestly I don't think that would be a serious problem. They still got a little cash. Besides, usualy the card shows a current date, its just been canceled. That way its not a current account that could still be comprimised by having an actual account #.
Some people want to tour with a gun as protection, I am not that scared. Half of staying out of trouble means using your wits anyway. While some criminals are dangerous, I have found that there are no Lex Luthers in prison or operating on a low level of malfeance.

I agree with others, $100 including perhaps $20 in small bills is a good thing to have. Some places like campgrounds might only take cash and gives you a back-up in case your debit card is lost. Another example is some stores have a minimum purchase so if you want to buy a soda and little debbie, you might have to use cash. Plus using cash for small purchases helps small stores with expenses.

Just to be clear, I thought that a dummy wallet was already a pretty high level of over thinking "the worries of the road". My comment was only intended as food for thought for those who are already worrying too much. My recommendation is to not worry about it at all beyond whatever normal precautions you would take at home. I figure that, where I tour at least, the risk is quite low. I also figure that the amount of money I carry and the cards I carry constitute a minimal and acceptable risk of loss. I bet a pretty high percentage of us live, work, or play in a more dangerous place than where we tour. The rural and small town roads of the US are probably lower risk than home for many or even most of us.

I have not been to Ireland, but I have been to continental Europe.

I carry more cash, ATM machines are much harder to find. Also since my credit cards are not chip and pin cards (or EMV cards) I usually do not try to use plastic for small purchases where I would use plastic in USA for those smaller purchases.

When I travel to Europe, I am frequently in tourist areas. That means pick pocket areas. I carry a fake wallet, it has enough cash for the day and a couple credit cards that expired about 15 years ago for accounts that I have closed.

I have some pants made by Exofficio that have an ankle height pocket that is zipped. Unless you are looking at my feet, you do not see the pocket. That is where my passport and plastic and rest of my cash is. I do not think they make those pants anymore, I have not seen them for a few years.

This really depends on your accomodation plan. If your camping, particularly if you're stealth camping, that's lots of money. If you're staying in hotels/motels etc, they'll usually take a credit card, so again, lots of money.

I seek out B&Bs and similar in-home type accomodations which can run $70-$110 per night, and often only accept cash. This can burn through cash pretty quick, so I'll generally carry larger amounts of the stuff. My plan for my tour next month is to start with €300 each for my wife and I, and then replenish that in €300 increments whenever we're running low...that will use up most of my daily withdrawal limit on my ATM card.