You could also use popen(3) (instead of system(3)). But you always need to fork a process (both system and popen are calling fork(2)). BTW, if you have a CUPS server you might use some HTTP client protocol library like libcurl but that is probably inconvenient. Better popen or system an lp (or lpr) command.
BTW, printing is a relatively slow and complex operation, so the overhead of forking a process is negligible (I believe you could do that in a server; after all people usually don't print millions of pages). Some libraries might give you some API (e.g. QPrinter in Qt).
Notice that the lp (or lpr) command is not actually doing the printing, it is simply interacting with some print daemon (cupsd, lpd ...) and its spooling system. See e.g. CUPS. So running the lp or lpr command is reasonably fast (much faster than the printing itself), generally a few milliseconds (certainly compatible with a multi-threaded or server application).
Quite often, the command passed to popen or system is constructed (e.g. with snprintf(3) etc...), e.g.
char cmdbuf[128];
snprintf (cmdbuf, sizeof(cmdbuf), "lp %s", filename);
but beware of code injection (think about filename containing foo; rm -rf $HOME) and of buffer overflow
Of course, notice that library functions like system, popen, fopen are generally built above existing syscalls(2). Read Advanced Linux Programming