World Map Projection Help

[Adamfaculty]

I've been working on a world map of my fantasy world, set during a sort of Renaissance time. I've briefly marked out the land forms that i think look alright, its just a matter of projection i want help with. I am currently using Photoshop to produce the basic outline of my map. The final thing will be hand drawn. My map is supposed to be based off of this map:



However, i don't know how to make my map in that projection, with the large western and eastern hemispheres being shown, and the north and south being shown in the corner. I only currently have a square projection of my map, and I'm wondering if anyone would help my figure out how to change the projection of my map, into the hemisphere thing in the map above.

For reference, here is the square projection of the map i have been working on.


Any help would be appreciated.