Out of the four choices you state, and if you’re only serving an occasional dog, I like the idea of the griddle.  Hot dogs will keep in the freezer for an extended time and you can thaw them as needed days ahead.  Hell, offer the grilled dog and up sell a deep fried one for .50 more!  The latter is relatively unusual, and certainly not for everyone.  Wrap the fried dog in bacon and up sell a dollar.  There are many customers who will gladly pay more for something with more calories in it and brag about it all day to co-workers and friends.
 
I’ll be interested to hear how it goes over time.  Best wishes!