I have been diabetic for 18 years & have travelled extensively always: Asia, US, Australia, South America, Europe, Caribbean (I LOVE holidays!!).
I have never, even once, been asked for to show a letter proving my diabetes. I even flew UK domestic through Gatwick just a few days after the liquids ban was introduced when the airports were in chaos, still I did not get any questions.
I don't bother saying anything when I pass through security, if I get a random search & they get to my little bag with my insulin pens & blood testing meter in it, I warn them that there will be sharps in there as I am diabetic.
For the last two years I have been on an insulin pump. Most times I pass through the metal detector wearing my pump & it does not set it off, I just go through & on my way. The pump has occasionally been noticed, or set the detector off, so I just say, I'm on an insulin pump. No problem, they see them all the time & usually swab it for explosives traces & off I go. It was fun going through the full body-scan in Manchester recently. My partner watched a generic silhouette of the human body (representing me) light up with a big red square where my insulin pump was sitting on my hip, telling the security staff where to search me for contraband
I have never been told that I should have declared my insulin, back-up pens or pump. I have said in a loud voice to foreign speaking security staff (as we English do to foreigners

) "Insulin...Diabetic", & they wave me on my way.
I really wouldn't worry about going through security, even in the US where you might expect them to be paranoid.
Check the hand baggage restrictions re liquids for the airport through which you are travelling. Last time I checked, it said (for the UK at least) that you don't need to put prescription medicines in your little liquids baggie with your hand cream & toothpaste etc., it is exempt from that additional check.
I do carry a letter these days, it's pretty simple as AMBrennan says, but I only started doing so in the last couple of years. I never bothered before the pump.
Enjoy your trips.