Without some kind of drawing/image, this is very hard to suggest any approach to... My initial impression is that it will be very hard to do in a CF composite.
You are expecting it to handle a load of slightly above 10 kg perpendicular to the tube, without "bending" = Not possible, it will bend, question is how much you can tolerate.
With a wall thickness of 0.1 mm and a length of 35 mm ..
I could probably make such a tube from Beta-titanium --- I would not care to speculate on the price though ...

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