My tactic is pretty simple when it comes to stuff like this. Whether it's a funny voice, a tantrum or an attitude problem I expect to be approached in a certain way if difficult child or any other kid I am overseeing wants something. It sounds a lot like this:
"If you ask me politely I may say yes."
"If you stop whining I may be able to hear you, I can't hear you right now I am deaf to whines."
...tantrums I pretty much ignore and simply refuse to respond to.
In your case I would be delicate since your difficult child is only 11 but I would say something like this;
"If you want my attention/that snack you are asking for/to play that game (ect.) please ask me in the right voice. The squealing voice is okay for play but it isn't okay for talking to people."
The squealing may continue for awhile but if you stand firm your difficult child will quickly learn what voices you do and do not respond to. I've had this trick work with all sorts of kids in a lot of age groups, difficult child and easy child alike.
p.s. It would annoy me too!