It doesn't hurt to have longer rivets in there. I'd go with 3/8" at least.
Just be aware that using a rivet that is too long for an application can cause the rivet to POP before it gets proper tension on the parts being attached together. The friction of the mandrel head pulling through a long rivet weakens the "blind setting" prematurely.
fyi... I didn't even know what that "blind setting" part of the mandrel was called till I looked it up on Wiki! It is a reduced diameter right between the mandrel and head that breaks at a pre-determined setting.