Replacing stem on non-oversize bars I have a road bike from Circa 2003 and it currently boasts an ITM Millenium stem. The stem is a bit long for my liking at around 130mm and I was thinking of replacing it with a shorter one for a slightly more upright riding position.

I have a feeling my bars however are of clamping diameter 25.4 mm, although they may be 26mm as it is an Italian bike (ITM bars too). Shopping around I notice that pretty much all new stems are of the oversize 31.8 mm clamping diameter so I assume they won't fit my bars.

How would I get around this problem? I heard one could get shims to thicken the bars at the clamping point but sourcing them seems to be tricky.
25.4 ( or one inch ) is almost always an MTB handlebar diameter or a very old cheap bike. From 2003 and of good quality, it is almost certainly a 26mm handlebar. 

There are parts of the bike you can bodge without much concern and parts you can't. Anything in the fork/headset/handlebar area is not something you should try and "make work". If it goes wrong, you'll crash hard. 

You should still be able to find 26mm stems if you look hard enough. Here is a good source. 

http://store.velo-orange.com/index.php/components/stems/threadless-stems.html

They also sell the appropriate shims to use your bar with a 31.8 stem, but if it were my bike, I'd just pony up for a new 31.8 handlebar.