Pudge,
First, two questions......are you cal or test lab? What industry(ies) do you support?
The questions will not determine which AB (accrediting body) to use, but may have an effect on the accreditation, since cal and test do have a few rquirements that are different. Also, specific industries/tests may have specific needs that others may not have. A prime example for that is fire testing which has VERY different requirements than say, microwave calibration.
As for the question of controlling RH rather than temp.....what is the measurement?
Graeme posted a good link where you can find websites to several ABs.....I recommend checking out all ABBs, get quotes, talk to existing clients to see who gives the best service. Then make a decision.
Hope this helps.
Hershal