I think there would still be a Mexican intervention, but there won't be the empire building that happened OTL. Probably they show up, shoot a few things, march around and make sure that their loan payments get back on schedule.
That!
But if 1866 happens is not a sure thing here.
For one 1859 is likely to be butterflied away, so no Kingdom of Italy allying with Prussia - Austria is instead still holding one of its richer provinces - make that the Austrian army is stronger (not much but a bit is seemingly enough) AND the troops Austria has to keep in the South are likey with the North Army in this scenario.
In addition Bismarck waited with 1866 until he had Italys support, he might not dare to move in this scenario.
Indeed, will Bismarck even be in power?
During the 1859 war, Prussia mobilised, and it went very badly. This triggered some drastic army reforms, which in turn triggered the collision between Wilhelm I and the Landtag which in its turn led to Bismarck's appointment. No 1859 war most likely butterflies this away, or at least postpones it many years. So Bismarck's appointment is at least considerably delayed and may well be eliminated altogether.
I'm still hoping for a Republican France that would lead to war with the Austrian Empire over Italy, and Austria get beat big time.
And should they be no war, what would happen to Austria without the reforms that happen afterward?