Exclaims: Is it always necessary to use it when someone is exclaiming? Is "says" OK?

I try not to overdue the use of the word "exclaims" in name tags (although, some might argue that I do, anyway), for example:

"No!" John exclaims.

However, when I don't put "exclaims," is it understood due to the exclamation points and the context of the given scene that the character is, in fact, exclaiming? (Please note that I am not speaking of someone yelling, shouting or screaming. That's something else.) For example:

"No, Terry, no! Don't do it!" says John, very alarmed.

Is it understood, despite it saying "says" rather than "exclaims," that John is, in fact, exclaiming, given the subject matter, the exclamation points, and the fact that it ends with it being explicitly stated that he is "very alarmed"?

Thanks.