The canary wrasse (Halichoeres chrysus) is among the most laid back of the Halichoeres wrasses...very under appreciated fish IMO. He would be fine.
The Blue Throat fairy could be a problem. They are pretty aggressive and might be a problem with other fairy and flasher wrasses. How big is your tank?
I would not recommend a six line with any other wrasse in the tank....2 six lines? Sounds like WW3 will now commence.

. If this is a 14 gallon the only wrasse I would consider would be the possum or possibly a pink streaked wrasse. Might be a bit small even for those.