I disagree with this
BB is a satellite reg who will likely know the power of first in vigourish here and will be calling pretty tight
So I entered the stacks, blinds, antes and the 98/2 payout into wiz and started mucking about.
If he's a good player and knows how often you're pushing, he'll be calling pretty loose.
If he thinks you're pushing 100%, he'd be correct in calling 70%+ !
I doubt that would happen though, but even if he thinks you're pushing half the time here, he is +EV to call with a pretty wide range. 22+, A2+, K5+, K2s+, Q9+, Q8s+, JT, J9s+, T9s
So I'd say the crucial thing is what is your table image like. What range do you think he'll put you on?
I think he'll put you on pushing about a third of the time. In this case, he should call with 22+, A2+, K9+, K8s+, QTs+, JTs+ (about a quarter of all hands)
He might have you pushing a bit more often than that, but still only call with that range anyway (coz he can be good, but not perfect)
Plug this in the other way, with big blind calling % as 26.5 (and for arguments sake we'll say the small blind will not be quite so loose and only call about 12% of the time)
The result, this is not an ATC shove

It is a shove just over half the time (55.4%).
So my push range here (assuming I get 13 minutes to act and can crunch all these numbers) will be 22+, A2, K6+, K2s+, Q8, Q2s+, J7+, J4s+, T7+, T5s+, 97+, 95s+, 86+, 85s+, 76, 74s+, 64s+, 53s+