So where did the 5" x 5" panels you were talking about earlier go?Room for cells is - 10mm width x 2" in length× 3mm depth.
No budget and it will be used 90% outdoors
At the surface of the earth in bright sunlight at noon the power reaching the surface of the Earth is right about 1000 W/m². You are working with an area of (0.01 m)(0.05 m) or 0.0005 m², meaning that the power hitting your panel is going to be about 0.5 W. Current, the best commercial panels are in the 18% range for efficiency, so you will only get about 90 mW of power out of it under optimal conditions. Yet you want to use it to power something that needs around 2000 mW.
Do you see the problem?