Class 1 low voltage wiring in wall
Ok, Class 1 wiring systems NEC article 725.49 (A) sizes and use and (B) Insulation which give you approved insulation for sizes 18 and 16. If it is 16 or larger you need to use Article 310. I would forget the 16 and use 14 nm instead. If you decide on 18 or 16 the equivalent to thhn would be tffn. Or I would check with whomever the manufacturer is and find out what they suggest. 

Hope this helps