Hello NtinosFerret,
It depends on the complexity, style and degree of realism you’re trying to achieve. As you stated, you don’t want to use volumetric clouds. I’d like to point you towards Inigo Quilez, although I don’t know how knowledgeable you are with shaders, his works might get a little bit complicated.
Also ClockworkOcean gave you a good hint, you can look into the default sky shader (it’s called ‘M_Sky_Panning_Clouds2’, if I’m not mistaken). They use multiple textures to create the shape of the clouds, you can adapt and change this, I strongly recommend creating a new material. You can change this behavior so the textures pan into different directions and multiply them to create a ever changing noise and work from that.
If you want further resources on how to create clouds, SIGGRAPH articles or research papers on real-time 2D clouds would be a good starting point, but I don’t have any on hand right now; maybe the paper from Mark J. Harris on ‘Real-Time Cloud Rendering for Games’, although it’s quite old it can give you a push into the right direction.
That said clouds are pretty complicated, and have been studied for ages. To achieve the best results possible you might have to go the volumetric route, however this might not be possible or feasible depending on your target platform. If you, despite that, want more information on volumetric clouds, you can look up Guerilla Games’ Nubis system (SIGGRAPH, their blog), which is their cloud and weather system from ‘Horizon: Zero Dawn’.