Well, this generated a great deal of interest...
I thought it was worth a fair amount of thought at the table, anyway.
It doesn't matter much what you throw from dummy, but you seem to have two options from hand:
i) Keep all 3 clubs (and if so, I think you should throw a diamond, not a heart: if hearts are 3-3 you can then choose who to play for the CQ).
You are now making if LHO has the CQ to any length, or RHO has singleton Queen, plus minute extra chance (hearts 3-3 and you correctly choose to play RHO for the CQ).
ii) Throw a club from hand. You are planning to cash hearts next, and if they are 3-3 take the AK of clubs followed by, if the CQ doesn't drop, the diamond finesse (or in some cases a show-up squeeze).
Compared to (i) you lose when LHO has Qxxx or Qxxxx in clubs, but gain when hearts are 3-3 are RHO has CQx, or hearts are 3-3 and RHO has the rounded queens.
I haven't worked out the odds, but they seemed quite close at the time.
Anyway, at the table it didn't matter, because the full layout was:
I discarded a club from hand, and LHO, who didn't fancy opening up a red suit, switched to a club. I put the 10 in and was not best pleased when RHO discarded (as I had 9 easy tricks if I'd kept all 3 clubs in hand). All was not lost, however, as after winning the club in hand with the ace, cashing 3 hearts, playing a club to the Jack and the king of clubs, RHO was show-up squeezed in the red suits and I could drop the DQ offside.