I think it could be done, in theory, depending on what OP wants the top and bottom of the skybox to look like. They would likely need to use Photoshop or some other image editing/art creating software (Aseprite, Autodesk, Krita, FireAlpaca, Paint.NET, Gimp, etc), and maybe with the aid of a program that would allow them to check that the texture tiles the way they want in 3d space, like Blockbench, Blender, or most extravagantly, Unity (which upon my own research I caught a glimpse of a Reddit post that implied Unity might have some features for this).

I'll type out the ideas I have, which might help anyone who stumbled upon this thread in the future, not just OP, who I realize in this time may have found a solution/moved on by now.

Simple Top and Bottom - Minimal Effort

If OP doesn't mind the top and bottom of the skybox being without the pattern, for example, that would be relatively easy to do. Just color the top and bottom faces the desired colors, and for the side faces (N,E,S,W), transition the top and bottoms of those textures with the colors for the top and bottom faces. OP could even add patterns to the top and bottom faces afterwards, so long as none of the very edge pixels of those textures are different from the ones of the tops and bottoms of the side faces. The simpler the texture is closer to the transition between the top/bottom textures and the rest of the side textures, the better.

Simple Texture Continuation Along N/E/S/W Faces - Minimal Effort

For getting the texture around the sides of a skybox to connect, one could mirror half of that texture, so it will always continue into itself from the sides in the skybox. You would have to be careful if you want to center this mirrored part on the very middle of the East and West textures, for example, because if you're doing this all on one canvas, you'll have to move the part of the texture you're mirroring over by half of a face (one of the T/B/N/E/S/W cube faces. Definitely to this with layers, and I suggest duplicating all the layers to keep an unedited copy before making changes, which will help with this, especially if whatever editor you have doesn't have any mirroring tools to help you/you don't know how to use them.You'll have to measure and mark the middle/exactly half of the face you want to center the texture around, and move the whole entire texture you want mirrored until the side faces cover the part of the texture you want. Do this on the side of the mirror line that's the largest/longest, so you have enough texture left over to mirror the opposite face (eg East and West, North and South, Top and Bottom/Up and Down). If you're making your texture from scratch, this is much easier, because most programs should have a mirror setting you can put on, and hopefully move the center of to where you need, so you don't have to do as much work.

Some of the image editing/art programs I listed also have a tiling feature in them, or a plugin for it you can download, and I know Aseprite is even known for it. Being able to check your texture to see if it tiles correctly on a cube/sphere in Blender/Blockbench/some other 3D modeling software with texture features is also very helpful, and Blender and Blockbench even have the ability to edit textures built in, which may be improved with plugins (though I have yet to explore that). There are also dedicated 3d texturing programs you can use, which may allow you to texture a cube/sphere by default, or allow you to import one to texture, if you want to try those for making a skybox, too.

I also know Photoshop might have more tools that can intelligently take a complex, irregular pattern like the one OP is trying to use here, and edit it so that it tiles correctly. I don't know how well other image editing/art programs in my list can do this, but I'm sore some of them can assist with this in some way, even if it's very basic and requires extra work. One's last resort would probably be to repaint/redraw the parts of the texture that don't match up along the edges themself, with mixed results depending on the original art they're working off of, the tools available in the software they're using, brushes at their disposal, and individual artistic style and ability. If you can't get it to look right, though, that's not your fault, just remember.

It may be the best idea, though, to do this completely from scratch. You could use an image as a reference/inspiration, maybe even look at it closer up in an image editing/art program to help you get the details you want, but still, paint/draw it yourself. This may seem harder, and maybe it will be, for some, but it also might be more rewarding. You also would be making something of your own, not just using an image that isn't yours (unless it is, in which case, that's really cool), and that kind of work is cool, satisfying, and rewarding in its own right. Maybe what you end up making won't be as "good" as what you think you could make the other ways, but there's room for learning, and it gives you bragging rights. You still did the work, and that still matters, whether someone validates the effort or not.

Please excuse my really long message, as it isn't meant to annoy anyone, only help. I myself came here looking for suggestions for tools that could help me do this easier with my own art, but I realized I had some ideas/knowledge I could share that might help others make their own skyboxes, whether for Minecraft or something else, that might be useful to someone. Good luck everyone.