The calculated Watt-hours required to drive the LED is 2.75 Wh, considering peak sun hour is 4.5 for most places in India, the solar panel size shall be as follows:

Considering the Battery Efficiency 90%, the effective Wh required  = 2.75/ 0.9 = 3.05 Wh

Sun Hours = 4.5 Hrs

Solar Panel Wattage = 3.05/4.5 = 0.679 W

So we need a solar panel larger than the above-calculated value ( 0.68 W ). The available area in my enclosure to place the solar panel is 60 x 60 mm2. The suitable voltage for the solar panel to charge the 3.7V battery is 5.5V. There are many 5.5V solar panels available in the market with this standard size, the typical wattage is in the range of 0.4 -0.45W. 

Finally, I decided to use Sunpower solar cell to get the maximum possible wattage ( 0.55W)  within this limited area. Following are the specifications of the Sunpower Solar panel, that I am going to use in my final product.

Sample Picture Of Sunpower Solar Cell:

Solar Panel Layout:

1. Top Side

2. Back Side