With the side bits of wood out that the shelf was screwed into it currently looks like this.

Can you take a pic from further back so we can see where this is in room. That look like a space under a cooktop not an oven

We have a very short drawer under our double oven and it's taller than that space. Perfect spot for pizza stone and 2 peels but that's about it.

It's a cabinet where the oven goes into. The oven could do with being moved a bit further up a few mm anyway,so it sits underneath the worktop without a gap.

Hoping to get rid of the 2 bits of support wood which is holding the shelf which has the oven on top and use some brackets to fix the shelf to the sides of the cabinet instead.

Obviously a bit worried if it'll hold the weight.

Look at your cooktop specs carefully before you move your oven up. Many models have specific clearance requirements between the cooktop and oven, to avoid overheating cooktop electrical components.