Several points from the comments above:
1. I surely would not assume that a 3
♥ bid denies an outside A or K. It would be rare that partner held one, but I would never rule it out, absent express agreement (and I'd never want to play such an agreement).
2. While it may be possible to play that 4
♣ asks for a feature of some kind, I don't think that this treatment is at all popular. In several partnerships, we play that 4
♣ over all 3 level preempts (except 3
♣) is keycard, with modified responses, while other new suits are asking bids. This asking bid approach is, I believe, very popular. The response structure is up to you: we generally play OKSVA: zero, King, stiff, void, ace... but other acronymns work reasonably well
3. On the given hand, even if partner has a stiff
♠, where do you think 12 tricks are coming from? Even if he has a
♠K, by enquiring about it, you are directing a minor suit lead, which you don't want unless he has shortness in that suit.
So just bid 4
♥.... or maybe 3N... which rates to make easily...I'd go with 4
♥ expecting to make 5.
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari