CO2 needs heat to give power...barrels are a heat sourse..so shortening the barrel will deprive the CO2 of that much heat for liquid-to-gas conversion, and end up losing bit of power. Wish I could tell you a magic number...can't, too many other vriables...but a guess would be about 30-60FPS for that 3" of barrel.
So far as I can tell, those barrels aren't choked (slightly smaller at the muzzle), so if it doesn't happen to be enlarged at the point you choose to cut, shouldn't do a lot to harm accuracy (of course, that depends on how well you crown that barrel stump too).
OF course, you could do a tune and get that velocity back (and ignore that it would have been even faster with the "extra" 3' of barrel that got chopped off).
Will certainly make it a bit louder...maybe not objectionably louder. Noise comes mostly from the exit presure of the gas/air that dirves the pellet, short barrels generally have the gas exiting behind the pellet at higher vel. than longer barrels, so they are usually a bit louder.
(that last is hard to judge by yourself. A lot of the noise is conducted to your ear through the stock you have your face pressed against. Same reason your vocie sounds "different" on a recording...recording doen't get the sound of bone conductivity that your ear does.)