There are three chain tensioners, one on each chain. You'd need to use a stethoscope in order to find the noisemaker. The main chain tensioner uses a ratchet as you mentioned, but the #2 chain tensioners do not.
I've had oil filters with (suspected) defective anti-drainback valves cause noisy cold starts. Likely the #2 tensioner(s) but I didn't dig in to locate the source, just changed the oil filter and added oil to top off. Noise gone.
So...what oil filter and oil are you running?