To answer your question, I don't think there's a law that forbids the use of slingshots. They are used everywhere. As long as you don't use it to attack someone
or to destroy something they are ok. Based on my experience it may happen like this: Either a policeman sees it and stops you to use it with you and play with it a while and then tell you its very good or something and let you go; or he likes it for his little kid or himself and says it's illegal and take it away from you to keep it to himself. The other option is he wants money, if you don't have it then he takes the slingshot to try to sell it later. I don't think they would put you in jail for it. That is for regular police.
They you have the army... Never know what may happen with them...
Now the rural police, they check for poachers. You may have problems with them, if you find any. But they have all been killed or they have fled from the field because of the drug cartels. That's why nobody goes fishing or hunting any more. It's not safe to go somewhere that may be used for trafficking drugs.
Besides drug cartels you have the "Z's". They just want money, so they rob or abduct people, they are the dangerous ones. Who killed the seventy something found in Tamaulipas? They say the Z's but I'm pretty sure we are beginning to have "guardias blancas" people who think they are heroes and begin killing everyone in sight if they don't like them. I think you too in USA have of these...
If you have common sense you won't have any more problems here than you would have in the USA. We have bad people everywhere; just try to avoid dangerous situations. You may have a serial killer found you in your apartment or parking lot or school in New York city. "Cuándo te toca, te toca" When it's your time, it IS your time.