Both SDCC and Cosmic are C compilers, so you'd just use the C source files.
But:
All STM8 compilers use slightly different syntax for language extensions, in particular you'll have to make minor changes to the declarations of the interrupt functions, and to inline asm.
SDCC (and IAR) has better C standard support than Cosmic (and Raisonance). So the source written for SDCC might use some ISO C99 / C11 / C17 features not yet supported by Cosmic.
SDCC tends to generate faster code than Cosmic, so you might run into performance issues.