The simplest solution seems to me to be to create a Sketch on the thickness of the cylinder that needs to cut the other one, Convert the inner circle into an entity and do a Material Removal to the next surface.
If it is not imperative to have separate bodies, you can make full extrusions all fused together and then end up with a shell function. This will make you all the intersections in one go...
If you are looking to simplify 2D later, you will be right to use the mechanically welded function because it will be recognized in your drawing.
The mechanically welded function is made for this design tupe and it would be a shame not to take advantage of it!
And since it is a mechanically welded, several solutions, personally I like to work with disjoint volume bodies (I am on Catia at the base, this explains it) for this it is enough not to merge the results.
I then use the intersections (most of the time) or combine functions (which offers you 3 types of results: add subtract or intersection).
You can also use the adjust/extend option.
OR last possibilities but which are less 'professional':
* During your extrusion, extrude to the next surface
* or create a small solid inter and subtract
* Or make full extrusions and use the shell function
It should be kept in mind that the end result is achievable in as many different ways as there are SW users;)
But the goal is to have a simple, efficient, fast and as professional design as possible.
I hope my answer will bring some grist to your CAD mill.