After taking ♠A, declarer should cash ♥K and then take the finesse. Firstly, West very likely has six spades, so East is more likely to have the ♥Q. Second, if it fails, then all the trumps have gone, so there would be no danger of an over-ruff on the third spade round.
It is also important to notice that, despite the doubleton clubs in hand, it is correct to finesse twice – we don't lose anything if the second finesse fails, because we will be able to discard a losing diamond on the ♣A. But we are short of entries to hand, so when the ♥J holds, we should take an immediate club finesse (to the ten). Subsequently, we draw the last trump and repeat the finesse. As the cards lie, we are in luck – both missing club honours are in West's hand. We get to discard a diamond without losing a club, and we make twelve tricks.