How to automate a script execution on import actions? Basically, I would like a way to let the user select a file to import and then transparently execute a custom script.

Most of the time, I use Blender in a work flow. When I do some changes on my models in other programs (like a sculpt program), I would like to keep the work I've done in Blender (mostly materials and lightning). The mesh I import already has different materials assigned to different parts of the mesh like "skin", "hair", "cloth", etc... but I heavily modify and tweak them in Blender. When I reimport, the new imported mesh get a "skin.001", "hair.001", etc... which are really basic (mostly a diffuse colour). I then have to reassign every time materials myself.

I couldn't find a handler for Collada import and didn't find a way with modal operators.
Blender doesn't have these kinds of hooks, the closest thing you can get to this is to write your own operator that runs import, then your own code afterwards.

For Python importers you could customize the script to include your own functionality and in a few causes you could monkey patch the importer scripts. But basically this isn't supported.

See this question for more details:
Run additional code after user has executed and finished an operator