Do you think it would seem strange if I tell an employee at Chuck E. Cheese not to ask my kid if he wants to buy ice cream.
Why don't you want them asking your kid that?
I don't want my kid eating ice cream and he'll want one if someone asks about it.
You have every right to ask people not to speak to your child especially when you're trying to get them to eat healthy. Just ask the employee politely, don't get angry at them.
Maybe I won't mention it. I bet people won't care anyway. If they want to offer something, they'll find a way to do it.
It's okay if you've changed your mind about asking, but just know that you do have the right to ask as a parent. People should respect that you don't them selling junk to your child.