In any case, however you distribute it, it becomes a full-time job. You can part-time assign highly qualified coders (you don't hire any other, right?) to do it, which would only mean you'd have to reallocate their tasks, i.e. hire additional highly qualified coder, for example. Which would cost you, probably, way more than hiring a recruiter - and your highly qualified coders would be very unhappy to spend time on reading crappy resumes (and since they are unfiltered, there will be all kinds of crappy ones, outright liars, scammers and what not). And then you also need to get on the phone with people, arrange schedules, keep documentation and keep track of interview progress and results, etc. etc. It seems to me you seriously underestimate how much of a time sink it can be.
People invented separation of labor for a reason, you know. Recruiting can benefit from specialization too.