There is of course FIPS validation for US specific validation. For international accepted modules there is Common Criteria validation. With FIPS and Common Criteria you mainly verify the system rather than a component or algorithm.
For either you first have to think of which part of the system you want to verify. You'd also have to think of which level you want to verify (FIPS level 1 to 4, EAL levels 1 to 6). For the later levels you may have more and more requirements for design and development.
So no, FIPS is certainly not the only / prevailing authority. As usual, besides the US, there is the rest of the world to consider as well.
Of course to pass FIPS / CC evaluation you may want to use a certified implementation for hashing. Otherwise you may be asked to certify your own solution. How hard this will be depends on the level.
Passing FIPS / CC is hard and expensive. You probably want to make sure you've got a business case before trying to certify an implementation.
Nothing stops you from trying to comply to FIPS and CC without certification of course; both do require you to implement your protocol carefully.