I think I have found a way to safely farm animals without taming them first. You have to build a structure I call a breeding pit.
Start with a short tunnel, about 8 tiles long. You need to access the end tile from above, so plan ahead and make sure there's room on the next floor up. The end of the corridor is the future animal pit, and it is closed off from the fortress by a lever-operated door or floodgate. Most of the corridor is taken up with cage traps. The other end of the tunnel is a lockable access door.
Dump mama and papa critter in their new 1x1 home. Wait for nature to take its course. Once the kids are born, you lock the outer door, and pull the switch for the inner door. The happy, feral family will run out and get caught by the traps. The ideal number of traps is the creature's maximum litter size, plus two. (Plus one if you depend on spores.) Once you have them all captured, unlock the outer door, and collect your captured animals, neatly sorted out one to a cage.
Bonus: Move the exit door over to a diagonal, and build a fortification at the end of the tunnel. This way, if a critter doesn't get trapped for some reason, you can station a crossbowdwarf at the end, and let him shoot the extraneous animal.
Bonus Two: Add a standing spear trap to the drop zone, and link it to a lever. This lets you turn your breeding pit into an execution pit with one lever pull. Make sure you keep track of which lever does what!