replacing wheels on a hybrid running on 700c
Brakes, tyre clearance, and lowered ground clearance are the three points.

If you have rim brakes, give up now.  They simply will be wrong, and buying super-long reach brakes will be expensive and won't work very well for leverage reasons.  Disk brakes may work okay, provided the rotor lines up, and your fork spacing is acceptable.

Tire/Tyre clearance should be okay because your new rim would be smaller.  However 26" tyres are often 1.75 or 2" so there may be clearance issues.  You'd probably have to go for smaller and not knobby tyres.

The bike will be sitting lower to the ground now too.  This will increase the chance of pedal strike going around corners, and the break-over height will be less, so you could strike the big chainring on the ground easier.

Surprisingly the wheelbase length will not change.  So "handling" should be unchanged.

Finally, the aesthetics will look somewhat weird, but that's only a visual thing.