I don't know about slingshots, you can ask a staff member about the specifics.
Try e-mailing this address, they know about rules and such (or they'll direct you to a specialist): policies@kumoricn.org.
As for guns, I prefer to use
cap guns instead of air soft. Primarily because I can just remove the bullets, remove the trigger altogether and glue down the barrel so nothing fires. Cap guns are cheap plastic toys and are easier to censor and pass through the prop check. You can go on Amazon and find a variety of styles and use those with your cosplays. Also, it really helps make things easier if you buy cap guns that have the orange tips on the end - which prove that they're plugged or fake, and are safe.
Trust me, cap guns look just as nice as air soft; so don't worry about walking around with some cheap blue thing that makes your pictures look bad.
As for swords and staffs, so long as they're not sharp or too heavy, they should be okay - just let them look at it and judge if it's safe so they can peace tie it.
Also, and this is very important, you MUST bring your weapon props to the table every single day that you plan to carry them with you in the con area. Prop checkers at the table are required to re-check all weapons to make sure they're still safe and haven't been modified to fire or anything. Each day, there's a new colored peace tie being tied to props. So, Day 1 could be blue peace ties and Day 2 could be green ties, for example. I learned this last year, and also found out that some people even collect the colored ties for fun.