Blend order: Most modeling veterans know this, but I put together an example for noobs. See picture below. In the 'favorable' method the vertical edge gets blended away then in another feature the top gets blended. The order is reversed in the 'unfavorable' method. The top 2 edges get blended first and then the vertical. You can see the difference in the surface type, bspline vs torus, and you can see the effect on tolerances. The bspline is 3 sided with 1 edge degenerated to a point. This degenerated edge can be pain point, especially with offsets. Another thing to keep in mind is: that you can assign different radii to different edges inside the same blend/fillet feature. When you do this to my example, occ builds the favorable method. So the modeling kernel knows which method to prefer.
That being said, the real world is not so simple. In the context of this part, there is a tendency to use the 'unfavorable' method as that is how it was originally done. However, we don't know why it was done that way. I am guessing that was the only way to get it through the modelling kernel. So with that, I would use the 'favorable' method, as long as I can build a valid model, and discuss it with the person responsible for the $.
I am wondering if it wouldn't be better to change the underside surface of the handle so the handle gets thicker naturally. This way the blend wouldn't be responsible for adding the thickness to the handle as it approaches the main cylindrical body. I might try that just for fun.