It is unlikely that anyone is going to let a couple of Ensigns walk on and conduct weapon qualifications. First, there's training requirements that you must meet before you even step onto the range that no one will have conducted with you. But beyond that, range space is often at a premium and you can't just say "Hey MA3, mind if I shoot a few rounds today?"
You will qualify for small arms when your command needs you to qualify for small arms. Make friends with the MAs or GMs and they might be able to get you in on the shotgun shoot if they have a last-minute cancellation. Otherwise, the guys who actually need to carry weapons to stand watch will be the ones who are going to the range.
There are some places that offer to do the qualification for a fee, but you're a special kind of stupid if you actually pay for small arms quals.