I find it quite incredible for such an old game that there is no widescreen fix besides a 3rd party hack-fix.

Before X-wing alliance they all had 2D cockpits which aren't exactly ideal for widescreen, if you mean X-wing Alliance, it's because they probably don't have the source code as Totally Games has been dead for several years and many features were essentially hardcoded, so it's either third-party hack-fix or nothing.

Where can I find this hack? Are the results good or bad? If they are bad, I like to stay with the original aspect ratio 4:3.
And for which game is that hack? X-Wing?

There's this thing here I've just found:
https://sourceforge.net/projects/xwahacker/
I have a 4:3 monitor so I don't have the faintest idea if it works well.
It seems it can also scale the 2D cockpits in X-wing vs Tie Fighter, hmmm, interesting.

What? No, it can't do anything about widescreen/cockpits for anything but XWA.
I don't consider the cockpit a major issue for widescreen, it would look a bit weird but you could just have the cockpit in the central 4:3 area and a bit extra view to the left and right of it.
The problem is that the game engines of these old games were never designed to run on anything other than an exact fixed resolution, and back then the decision what to show where was done in the program, not on the GPU, so it's not easy to modify.

No, I wasn't referring to the aspect ratio (I use a 4:3 anyway) but I took the "cockpit upscale" as an option to upscale the 2D cockpit to an eventual forced resolution, so it can't be done even with XWAhacker?

Assuming you refer to the "HUD scale" in xwahacker that still is only for XWA, not X-Wing.
And it is only about the actual size things show at.
If you don't care about the aspect, the ddraw.dll wrapper already renders everything at whatever resolution you use for your Windows desktop.
My fork of it has a ScalingType option to configure how to scale 2D parts like cockpit to that resolution, but for X-Wing at least it's a fairly marginal improvement because the cockpits are fairly badly drawn (not at a consistent resolution) thus upscaling them never looks great.
Things are even worse for the videos in X-Wing which randomly mix 320 and 640 resolution.

I was mostly interested in the feature for X-wing vs Tie Fighter (the game is still locked at 640x480 even using the DGvooddo2 wrapper), I always play the DOS CD-rom versions of X-wing and Tie Fighter, as my old CDs still work and dosbox is very easy to set up with a complete HDD install.

Of course I do have the windows versions as well (imported, of course) but I used them only back when DosBox was still a dream in the mind of some nostalgic programmer.

As said, all games in the series render at native resolution with https://github.com/rdoeffinger/xwa_ddraw_d3d11/releases/latest
Just widescreen (the subject of the original post) is not currently possible. For that the choice is limited to black bars or incorrectly stretched output.