Being upfront and honest is always the best solution. How embarrassed could they be compared to the constant reactions others have to them. If they constantly stink, then how many people must shy away from them because of that. Or, if they just finished working out and don't realize they stink.
Personally, I would want to know. If enough people are honest with them, maybe they will make a chance. Sometimes, it takes an embarrassing situation to get people to change their ways.
If you, personally, care more about whether people like you than doing what's right, then you may not be the one for the job. Ask someone who is more like me to do it. :)