It depends on who you're hiring, but the fact that you're there (or not) is pretty much irrelevant - whoever you choose still has to be there, on call, and not in their own bed guaranteed to be sleeping through the night.
I'd suspect you could find someone trustworthy who'd be willing to do this for $50/night plus the hourly rate for any wakings (rounded up to the nearest hour, even if your son is only up for 10 minutes).