You can use any of Irvine's weapons to shoot any of the ammos. Squall is the only character whose Limit Breaks are dependent on what weapon he uses. Also, Pulse Ammo is used to make the Lionheart, so there is another reason to get it.
The undoubtedly quickest way to get Pulse Ammo is in Disc 3, after the Lunar Cry, talk to the Elnoyle, defeat it, and collect Energy Crystals. Ammo-R them, and ta-da!