"Reject" is similar to "detest" but definitely not synonymous. Rejection is usually a result of detesting someone and not the other way round. So, no. You would need both words.
reject verb
to refuse to accept, use or believe something or someone
Source: Cambridge Dictionaries Online
If you choose to use "shun", note that it means rejection in the sense of ignoring someone and not refusing to accept them.
shun verb
to ignore someone and not speak to that person because you cannot accept their behaviour, beliefs, etc.
Source: Cambridge Dictionaries Online
"Spurn" meanwhile is the other meaning of "reject":
spurn verb
to refuse to accept something or someone because you feel that thing or person is not worth having
Source: Cambridge Dictionaries Online
Thus, neither "shun" nor "spurn" carry the meaning of both "reject" and "detest".