Rearranging skills into all-new trees should be as easy (?) as editing PilotProperties.script, and if you refer to the pilot interface folders for tips you'll see code defining their trees as well as the graphics for them. They aren't in nice complete images, every single skill has a bunch of what appears to be coordinate definitions inside an .ini file, among other things.

The specializations themselves aren't really mentioned as such in the scripts; they appear to be simply a fancy way of asking the player to choose which list of skills Hero should have. I suspect you can mangle these four skill trees as much as you like short of actually altering how many of them there are. Why? Because displaying the names of the skill trees is actually hardcoded text in one of the short interface (.loc) files. E.g. for my missiles mod I wanted to display such useful stuff as how many warheads per MIRV instead of the total because a single total number doesn't tell you how many fragments you get, but there's simply no support for displaying additional variables in the interface.

The skills themselves are hardcoded to some extent as you can see in CalculatePilotSkills.script and perkDispatcher.script (as seen here). That's only for the passives iirc, I didn't bother looking up the actives, summons, etc since the game is being an ass at not caring about changes to the XML schema files.

Pretty sure you can toss existing skills but you'd need to grep the AI pilots script and make sure to remove/replace mention of those skills as well. Like for example if you wanted to ditch Gunnery_1 and enter a new skill called Badass_1. You'd need to edit out any mention of Gunnery_1 in the scripts and enter code to handle Badass_1. It might be more convenient to just hijack an existing passive skill - in that case you can leave the AI entries alone and just edit the code structures.

TL;DR: it should be possible to replace the specializations with completely new skill trees but you'll have to keep the same number of them (i.e. 4) -- and make sure to edit the code scripts to change the behaviour of the skills.

Edit: as usual, Goblin Wizard explains it better