Actually A9o is pretty close to wanting fold equity or not.
This is modelled in sit n go wiz, because as noted, it doesn't matter if we raise/fold or not - the outcome is you getting all-in against villain. What we can manipulate to an extent is his "getting-all-in" hand range.
Here we see with A9o, it's pretty marginal all the way. The only way we can really gain an edge is if we can induce him to:
a) get all in with a very wide (80%+ range)
b) fold extremely tightly
If you think open shoving will get him to fold tighter than like 5%, or 3x raising will get him to shove like 80%+, then take those lines.
Barring that, you might actually consider folding and passing up a 0.1% edge.
Important note is that this is assuming that villain can only do 1 or 2 things - shove or fold. He could flat pre, and then you'd have to do something on a flop. This of course could be advantagous.