I'm talking about the small slot around the cavity itself where the plastic cover goes into.
I don't have a router, dremel or a chisel. Does this even possible without any of these? Maybe with a blade, sanding paper and patience?
If not, since it's really cheap, can a chisel help me with this?

Help please
I highly recommend having a router, there's no other method that would work with good results. A dremel would be my second option but it would be very tedious and require a steady hand to yield good results.
This is the best way I can think of, albeit slightly complicated.

Screw your cover down where you want it, and use a sharp scalpel blade to mark the outline onto the guitar. You can then put some fairly well-fitting MDF into the cavity, make sure it can't move around. Acquire the correctly sized hole saws or forstner bits for the rounded corners, and using a bit of geometry mark the centre of the circles onto the MDF. Drill pilot holes and then use the hole saw or forstner bit in each corner to the required depth.

You can then chisel the areas between each corner with a sharp chisel. You might want to widen and deepen the scalpel cuts a bit first. Be careful not to slip out of the groove though.

A lot of work there.
Unfortunately, I can't afford a router or a dremel for this project. Maybe in the future..

This method will work I guess but it sounds pretty difficult, especially since I don't have much experience with this. I think that I'll just place the cover on top of the wood so it'll stick out and save myself from this..
Thank you guys!