It just seems to me that using explosives on a structure where collapse is imminent in order to fix it sounds like the most dangerous idea one could possibly have.
First of all, according to what the experts are saying, the most dangerous idea one could possibly have is your idea of doing nothing - that guarantees the worst-case outcome.
Second, one would normally expect the force required to break the dam to be orders of magnitude larger than that required to open a sluice gate. Obviously this isn't a normal situation, but then, what are the figures? If a stick of dynamite isn't the appropriate tool, exactly what would it take to open the gates?
Third, if you could say 'we are going to try this at such and such a time, everyone be prepared' that would be far better than having it fail at an unknown time.
Fourth, now that I think of it, even deliberately blowing up the dam at a known time would be better than letting it fail at an unknown time.
Fifth, I'm sure there is some relevant idea or consideration I haven't thought of, that someone else could think of if they put their mind to doing so.