I'm confused about who it is you're afraid of slighting.

I usually back away from these situations where my social life is involved, saying that I don't have time for the job. Better a stranger criticise, and no hard feelings.

Sometimes I blame myself to the person, by explaining that I'm perversely dogmatic and therefore can't help but find fault. I can make my "extreme uptightness" a condition of my doing the work, and then if they accept it's cool, and if they decline it's cool too.