I would have assumed that you don't want to use uint_fast16_t to store anything that doesn't fit in 16 bits.

If you cast to signed that can't represent the complete range that still wouldn't be called "overflow" AFAIK, and no matter what you call it it is not "undefined". And assuming 32-bit ints there is no loss of information given a 16-bit ints.

You can also just cast to unsigned or whatever type you think is enough (you should know). The point is, use a conversion, cast to a simple type, make your code compatible.