Although I agree with Rustle's process in that there are very very few situations that require and instant response. A MEP single engine failure in the cruise probably is not a 'panicable' event, something like fire or ice being examples of the exception.
However, once you have assessed the situation, taken appropriate action and reviewed it and then you still only have one engine, a Mayday and a divert seems to me to be an eminently sensible course of action. In such situations there is no sense in considering others, that is ATC's job. One needs to keep one's options open and it costs nothing. It is always possible to downgrade later, but I imagine that it is potentially much harder to escalate if your situation suddenly deteriorates.