Place tell me , 3d printing , 4 axis laser or other.
Some methods I can think of, all suboptimal:
3d print something in flexible filament and wrap it around your gourd. Note that printing with flex is already an advanced topic, and you’d need to glue your print into place. Similarly, you can laser something from a thin, flexible sheet material (like paper!) and do the same thing.
If you insist on marking the gourd directly, CNC could make scratches in it, but you’d have a difficult modeling job to do and you’d have to spend a lot of time “milling away” thin air. You’d need the rotary axis for this.
The only way I can think of to make the laser act directly on an irregular gourd is to break your design into separate bands that each get burned onto a strip of gourd that has a fairly constant radius. Some gourds, and some designs, would be more accommodating of this than others. (You’d also need the rotary axis here.)
Really, if your main use case is drawing on gourds, you want an Egg-Bot and some permanent markers, not a Snapmaker.
I often laser engrave (10W) highly irregular vases and clay items with the rotary module. Works like a charm as long as the irregularity does not exceed 20% diameter on any specific point (then, it will get out focus or worse, hit the laser module).
So in short, sure you can laser engrave gourds with a bumpy surface, unless they are bend really strongly like a banana.