The specific handling changes you will get come from two effects.
First, lowering the front puts your weight further forward, and tilts your torso down. You'll find the bike tends to "dig in" more then you go down into a dip or rut, and you're more likely to go over the handlebars as a result. You'll also have more weight on your arms, so you're likely to find the bike less comfortable on longer rides. You might also have more neck soreness since you're looking up more when riding.
Secondly, you've changed the head angle and trail. A steeper head angle normally makes the bike more twitchy (responsive to steering input), but since you also have more trail (if you extend the line through the head tube to the ground, and measure back from there to the centre of the contact patch, that's the trail). More trail means more castor effect - the steering tends to return to centre if the bike is upright, or turn in towards the direction of lean. The combination is likely to make the steering feel heavier, and you'll have to work more to keep the bike on track if you're not leaning perfectly on a banked corner. On a flat track when cornering the bike will want to oversteer, twisting the handlebars into the turn until the wheel flips sideways and you crash.
The change from 29" to 26" is relatively small, so the above effects are unlikely to be dramatic, and you will probably be fine. I expect you'll ride for a bit, re-read this answer and go "yeah, it does that, a bit".
You could eliminate the first effect by buying a stem or bars with a bit more rise in them. You're going from ISO622 to ISO559 (bead seat diameter (BSD) in millimetres), or a difference in diameter of 63mm, so the bars will drop about 31mm (assuming tyre size stays the same). A stem 30mm higher should be fairly easy to find.
This assumes you're using disk brakes, since rim brakes won't work with the smaller wheel. If you don't have disk brakes, the missing front brake will be the main thing you notice. You'll lose 70-90% of your braking power, and that's bad.