I was in the exact same situation you are. I was not sure to start a South America trip with my 1995 KLR with 45 000 kms. After collecting alot of info, I went for it.

The KLR is extremely simple and does always work. There is not much that can go wrong.
I have the C-Model, like you have. ( we are from Switzerland as well ).
There are altough some downsides:

- Oil consumption! My bike used around 1 liter on 2000-3000 km at the beginning. Now I am around 1 L on 1000 km. Very annoying !

- The famous Doo-Hickey. It is simple to replace.... and you can forget about it!

- Specially for the C.... no wind protection ! Not that bad, but in Patagonia it was really annoying... so I built a simple home-made-thing .

- Tank range... I have the Acerbis 25 liter tank. Sadly It is almost impossible to find.

...the rest just works .

Some Tipps:
-Take a clutch cable
-brake pads were easy to find in argentina
- the Hepco and Becker racks are super !
- dont worry about the frame bolts.... this flaw exists only in the US Models.
- If youre Bike uses alot of OIL, go with the DR or buy a Wössner Piston ( around 160 euros, it will stop OIL consumption)

It is a awesome bike..... and I would take it again. I should have done the Wössner Piston work though

Here is our blog with alot of pics: locos en motos !! Mit XF650 & KLR650 in Südamerika.