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.