How to get a smooth transition between two objects. Two perpendicular cylinders

I'm trying to create a smooth transition between 2 objects. I thought I would start simple with 2 cylinders.

In the image below, I have created two cylinders, one slightly smalller than the other. I have simply used a boolean union, which I have applied. After this I have used a subdivision surface, to give it a smooth transition between the two. The issue as you can see is that it creates an undesired optical effect.

I've tried using a bevel, which just messes up. I've tried using a bevel modifier, which works at a very small scale. I'm looking for something like the hairdryer image attached - a smooth transition.

Am I modelling this the wrong way? If so, what would be better?

3. add the Shrinkwrap Modifier to the handle, selecting the other cynlinder as target and using the created vertex group play around with the Mode to suit your needs).