OP asked for a feature that I hate. I gave him a link of mouse that exactly has that feature.
How the hell it isn't answering the question?
Mouse with separate scroll wheel and middle button
summary: http://www.logitech.com/en-us/mice-pointers/mice?filters=3374
Every single one has that stupid feature where I can't click the middle button, which is exactly what you want. They have another middle button but I like to use that for gesture.
Maybe I should mention that the feature name is hyper fast scrolling. Also I have filtered logitech product based on that feature.
I already added another answer that is more correct.
The problem is that there are several products that do match what the user want. The one I am using is mx anywhere 2. Even though many says master is better.
Here's the issue. I narrowed it down to 2 product. One is the one I actually use. Another is much more expensive but better. How the hell I was supposed to know which one is better for OP?
Why is it wrong not to recommend one single product if there are indeed many products that qualify?
Also the question problem is that they accidentally click the middle button. When the scroll wheel is clicked it doesn't register the middle click. So his problem is solved. Clicking the scroll would simply switch to fine scrolling. It's not even a click. It's more of mode switch.
I noticed that a person need to press half centimeter to switch to fine scrolling. I didn't notice that. So yea, no way of accidental click there.
Why don't you let the OP review my answer rather than censoring it? I think my recommendation would be useful for OP. If there are better mouses others would have answered it.
If you have issues with my answers you can just downvote or put comments. I think that issue can be solved more easily rather than deleting answer. I can then update my answer based on comments and what OP truly wants.
If you delete answers, OP doesn't even know someone is answering. His question is not answered. How can he found his mouse?
If my answer doesn't perfectly answer what op wants, he can comment, other people will recommend other mouses. He's "going somewhere".
I think what I recommend is already a very good start.