If you use the immediate action to start a grapple, is it at -2 CMB or -6 CMB (because you need a hand free for the style)?
As I read it you don't need a hand free for the style per se, only to get the shield bonus. So when you go to grapple, you can choose to use one hand (keep shield bonus but -6 CMB) or two (only -2 CMB but lose shield bonus).
Related question:
Can you use feat when it does not do anything?
E.g., can you use Dodge if you are denied doge boni? Do you count as using the dodge feat?
Or, are you using the Snapping Turtle Style feat, if it does not grant you any boni, bacause your hands are occupied?
To start using Snapping Turtle Style you used a Swift action to enter Snapping Turtle Style. After that I think you're using Snapping Turtle Style until you stop using it or combat ends (maybe being stunned or paralyzed stops a style too - I'd have to check)