It's good that you're replacing your BB - lots of people aren't aware that square-taper cranks need to be matched to specific spindle-length BB's in order to get proper chainline.
As to your question, there should be no problems putting a 113mm BB on the bike, provided you get the proper type. I assume - since you have a hybrid bike - that it's an english-threaded 68mm shell (by FAR the most common).
The only issue I can think of: chainline. I assume that the MTB crank was designed to work with a mountain bike's 135mm-spaced rear wheel. If your hybrid has 135mm-spacing, then use a 113mm bottom bracket. If the hybrid has 130mm rear-wheel spacing, then you'd want a bottom bracket with a shorter spindle.
But I'm pretty sure most hybrids have 135mm-spaced rear wheels so you should be okay.