You can write a C code without using a header function. This means that you need to write a program that does not come with header files. Take note that you need to provide manual declarations that will allow the program to still be used. If in case you would like to run a C code without the header function, this is also possible but you may be looking at an interpreted script instead of using a program perse.
A lot of people are expected to use the header files anyway because they do not take up a lot of space. At the same time, they can also provide a lot of modernization that you may need for the type of program that you are creating.