At any form of scoring, the big issue is that you care
which aces and kings your partner has, not just
how many.
Playing 2/1, I would bid 1
-2
-2
-3
and expect partner to begin cuebidding: 4
from partner, 4
from me, probably a 4
attempted signoff from partner, 4
from me, and now partner tells you whether it's the CK or DK he has. (If his only king is in spades, as you fear, at least you get to stop in five, though there is a risk that's already too high.)
Playing SA, you will run into an issue as to whether 3
is forcing or not. (I feel strongly it should be - but accidents happen with unfamiliar partners.)
The 4NT bid has flaws - potential 2 fast losers in clubs if partner has one ace, and not knowing which king - but if you're playing SA with an unfamiliar or beginner partner it may be the best you can do in practical terms.