I would 3bet/ get it in 100% preflop vs this SS. That said, if you are going with exactly the range that you gave him I can't see any other option than folding. The player you describe is definitely never barreling with worse than AQ here (I also think he has AJ in his range but that still beats us).

SSers are generally going to be stacking off preflop with like AQs TT+ and 3betting/getting it in simplifies things. Additionally, if you have such a defined range as the one given AK is going to play absolutely terrible post flop. This type of player is going to be folding all under pairs on Axx flops and the only flops he stacks off with under pairs on are the ones that miss you. By 3betting/stacking off you at least get to see all 5 cards instead of c/f probably around 80% of the time.