If there are People who want to try creating even better skybox textures for the game, here are 2 tutorials :
Tutorial 1 : This video tutorial explains how to replace the skybox textures in Max Payne 1 :
For example, here are a few examples of what you can do with this method (Showcase test) :
The customized sky and skyline textures in my mod Noir York City for Max Payne 1 have been created with this method (Sorry if the video is a little too dark, but Max Payne 1 is very old and it was complicated to record it correctly. That said, the video is bright enough to see the visual changes).
Mod Noir York City v1.5 (Showcase video - What you can do with more advanced textures modding) :
Tutorial 2 : This text tutorial also explains how to replace the skybox textures in Max Payne 1 (It is for use in complement of the video tutorial) :
NB : And when I have the time, I will try making a tutorial which explains how to replace the normal textures (like for example the textures which recover the buildings' walls and also items).