A little aluminum foil in the adjacent compartments in your billfold should shield and detune the antenna enough that it can only be read when you take it out to use it.
That should take care of all but the most creative thieves.
If you really do not care much about your card, I'll bet 10 seconds in the microwave oven will fry any rfid chip inside. Not sure if the magnetic strip will still have your code on it though. maybe put the card partway submerged in water so the magnetic strip does not heat up, but the upper part is exposed to allow bigtime currents to flow in the RFID receiver input.
Does shielding work? do your own experiment and find out. http://www.rfid-shield.com/info_doesitwork.php
I have heard that the cards can be scanned more than 3 feet away. http://www.trolleyscan.com/newslett.html This link was not the one that I was looking for, but does help back up the claim of over 3 feet. Just need a briefcase, with a high powered reader, to grab all the information from passing people. Not all readers are set to low power reading at 1 to 6 inches.
To disable the see through card that I have in my hand, cut the antenna that circles the out edge of the card. The antenna wires are up to a quarter of an inch from the edge.
Let me get this straight. You prefer a mag stripe that can be copied by anyone with a mag stripe reader against a device using advanced cryptography.
There have been massive amounts of fraud here due to thieves connecting their mag stripe readers to bank machines and similar places. They have already figured out how to get your mag stripe information. Realistically you can't protect your mag stripe data unless you can identify every make and model of reader and where they are legitimately used.
Also clearly you haven't bought gas outside in a Canadian winter.
If you insist on shielding there are shielding sleeves made for passports with RFID in the passports. I'd get one of these and cut it down to size.
At least that way you could actually use the card. I suspect without the RFID your card will declined as likely fraudulent.
My bank has yet to issue RFID credit cards to me so I have not seen one. My caution would be to be sure that the old magnetic "swipe stripe" is available or the card will be pretty useless except for 'net transactions. Not many business have the old card imprint machines anymore!
RFID is more a resonant tank circuit than just an antenna. Hence it is the matching circuit that is more important. Two suggestions 1 Mechanically break the circuit by punching a hole or taking a blade and cut the transmission line. Credit card is still valid. 2. The other way is putting near a heater. This will make the passive components (inductors or capacitors to unsolder) and then remove those components. Or if you are expert in soldering, you can slowly unsolder the capacitors and even carefully remove the antenna.