The CarbonEaze rigid carbon fiber plates or inserts are only 1.0 to 1.2 mm thick, so they can pretty much fit into any shoe except for the most tightly fitted shoes. When using them they will restrict the movement of the metatarsophalangeal joints across the ball of the foot and relieve symptoms that are associated with that movement.
There is not necessarily a need to go out and buy new shoes that are bigger to wear these inserts, unless you have those really tight fitting footwear like the soccer boots or cycling shoes. They are often more comfortable to wear in runner or sneakers type footwear as these types of shoes usually have an insole in them that you can place the rigid insert underneath.
If you do need new shoes, then consider getting a pair of running or walking shoes that have some sort of rocker in the front of them. As these rigid carbon plates restrict motion, shoes that have a rocker tend to allow you to move forward more efficiently and rock over the shoe rather than be able to bend the joints across ball of the foot.
The typical shoe that does this is the Hoka running shoes:
You can see the rocker in the front foot above that will allow a more efficient forward movement if you need to wear the rigid plate to restrict motion in the forefoot. Plenty of other running and walking shoes have a similar design feature, it is just that the Hoka one tends to be more extreme and so can be used to illustrate how the rocker may feel.