It has been done to death, but actually as tempting as it maybe, the radio is hardly the first priority in any event. Stabilise or resolve the emergency is what we are taught. In the event of a engine failure without warning (a very rare event) setting the aircraft up for a glide is far more important.
Frankly the only good a Mayday is going to be is telling the rescue service they need to look for you and where to look. Therefore unless you are at very low level having stabilised or resolved a Mayday giving your position will likely be heard by whoever you happen to be talking to even if you repeat the call a few times over the top of everything and everyone!
Personally I always know where to instantly find my GPS co-ordinates and I think it is good practice to make sure your eyes go straight to this information. It is all that really matters.
I also agree that an EPIRB is almost vital over the sea. Frankly once you have ditched you need some form of locator beacon as you will drift surprisingly quickly and more likely than not the aircraft will sink with varying degrees of rapidity.
However, to repeat myself, if you don't get down reasonably in one piece, all the Maydays in the world aren't going to be much help so concentrate on that part first - I know it is tempting to think otherwise!