I’ve grilled 'em whole a couple times. It’s a little heavy on the ick though. I par boil or steam them about half way done. I then yank the critters from the pot & put them in an ice bath, until they’re cool enough to be handled. Now for the ick…
Next, I split them all the way from the eyes to the tail and scoop out all the organs and other gross stuff in the cavity. I’ll then brush any exposed meat with butter and apply a healthy dose of cajun seasoning. Then they go on the grill for the final cooking.
I suppose you could do the whole thing on the grill. I prefer to have the boiling water play the role of executioner though.