How can I arrange an original tour around the Inle lake?

Go straight to the boatman,and explain clearly what you do (and don't ) want to do.You will need to negotiaite a price,depending how far you want to go and what you want to see.

A longer trip to the southern part of the lake is a good idea IMHO.

They may still try to stop at sellers etc on the way....make it clear you are not interested.

Thanks for your reply. That's what I had in mind, but do you have any advice on what to see in the area? I read about the 5 day market, which seems interesting. Any other ideas? My fear is that if I approach random boatmen asking for a less touristic tours without giving specific indications, they will take me exactly in the kind of places I want to avoid.

The market for sure,which changes location as you said.That was great for photos,lots of traditionally dressed locals,animals and products etc.

The far south of the lake...the water here is much narrower.You need special permit to get down there,which you can pick up on the way.There are some villages with temples and pagodas down there.

One of the floating villages on the way.And at least one of the floating gardens too.Up close with one of the small boats with fishermen (better at the start..early morning,say 8am or so).

I avoid the 'craft villages' and the more touristy monasteries (eg the cat one) but some people want to see that stuff too.....

First of all i dont find the normal boat tour a tourist trap, i have done it a few times and still like it even tough ... there are many people doing it nowadays. There are perhaps a few too many silversmiths now, but the lotus weaving and boat making is absolutely original and unique in Burma/Inle lake.
The special permit to get down to Sankar was dropped a few years ago when the inle zone fee was raised to 10$/ 12500 kyat. It is a long trip though many villages and no stops, 3 hours of sitting and just passing though village after village, bamboo forest, more villages, more forest until you reach the next lake, Mobye lake which is also called Sankar lake. Have a look at the map, Samka is the original name.
So if you want authentic get up early and go to Sankar. Or do a bicycle tour around and visit the places the boat tours never touch.

I didn't know the permit is not necessary any more..that's good.

I liked that end of the lake a lot more.Far fewer tourists and the boat is often up against the shores,so you see alot of local life,villages etc.

You don't have to do the shopping trip you can go elsewhere. You can book your boat through an agent such as Thu Thu Aung who I have used several times, she can advise on where to go and where the 5 day markets are. Sankar maybe worth it but will be quite a bit more expensive. Boat for full day on lake should be around 15-20,000 kyat thats for up to 5 people, Sankar I hear is around 60,000 kyat.

As I have read in other comments, tell the boat man exactly what you want and don't want to see. The lake is huge and you can customize your trip. I have been to the lake many times and although most of tourists and boats go to the same places, it is really amazing. For example, one of the tourist stops is to see how they work with lotus flower silk and it's really interesting.
If you want to avoid all tourist places no matter what, just tell the boat man so and enjoy the lake, floating gardens, fishing villages, and my favourite, one leg paddling fisherman: http://www.myanmartravelessentials.com/activities/the-art-of-fishing-and-one-leg-paddling-inle-lake/

Happy travels,
Juan

Thank you everybody for your help! I'll try to organise a beautiful boat tour :-)

I've also heard that renting a bicycle in Nyaung Shwe and exploring the surroundings of the lake is nice. A traveller told me that he visited a village where people make tofu and that is was an impressive experience, well worth spending one extra day there.