I've had similar problems; my solution is a bit more roundabout, but seeing as how you're considering building an aqueduct, maybe you'll like it?
Step 1: dig a tunnel to the stream.
Step 2: using walls and floors on the level above, build a little boxed-in area around the stream that's only accessible from the tunnel you dug to the stream.
Step 3: set the tunnel as high traffic, designate zone-only fishing and make a zone inside your bunker, and enjoy indoor fishing in safety.
Here's a few screenies to demonstrate my method:
In this shot, you see how I've built an artificial wall (at the bottom of the screen) to limit access to the outside world. I was fortunate to find a part of the stream that ran between two cliffs, but if you're not, simply build a bridge from your tunnel side to the other side, and build a wall on the opposite end. You'll notice my tunnel opens up from one of the cliff faces right onto the river. I'm lucky enough for this to be a brook, so I don't need to install a pier or anything, or even a bridge for them to reach the other side.
Since you only need a single roof, once the perimeter wall is done, build a ramp and then roof the thing using constructed floors, like so:
In the interest of not getting killed, I recommend making EVERYONE you can spare a mason; you'd be amazed how fast 20 dabbling masons will put this together. If you have a decent military, station them there for the construction.
It's a bit of work, yes, but I find it's both simpler to set up than an aqueduct and cistern, and carries no risk of Fun through flooding.
EDIT: if you're not above using DFHack to cheat, you could use their auto-dump program to help. Designate a bunch of stones you want to use for dumping, then use the program to dump them at the building site, to minimize hauling. I prefer to take the risk of attack, but just throwing it out there in case your style is different.