A countermark is part of the creation process of the coin, is isn't the end type of the coin.
Some countermarks turn coins into tokens: N#125720
Some countermarks turn one circulation coin into another circulation coin: N#53448
Some turn a coin of one country into a coin of another country: N#332598
Some turn a coin minted for circulation into a commemorative coin: N#67948
The last shows the flaw in the proposed scheme: We should distinguish between a countermarked coin that is a standard circulation coin and a countermarked coin that is a commemorative coin.
It would be nice to have the fact that an item is countermarked be obvious and searchable in a standard way.