You do need an FHA certified contractor for a FULL 203k.  There is now a limited (steam K) and Full K as defined by FHA.  Anyone can help you on a limited, but you need an FHA cert guy for a full.   
From your list, it could be either. 35k+ in repairs and/or structural work is usually the cut off for a full K.  Your loan officer should be able to let you know which you are doing, and give you a full list of approved contractors in royu area.   If your LO cant do both,  you should really find a different LO.     Working with someone thats is flying blind on a 203k can make the process absolutely brutal.