stretching world map to globe template?

Hey!

I wanna illustrate a world map myself to print it later and glue it on a globe. The thing is, there are templates to download, so its easy to cut them out and arrange them on the globe accordingly to the curve of the globe, but its more difficult to paint on them. Is there a more or less easy method to start with a flat world map, and stretch it later to a such template?

Here an example:

http://www.boehmwanderkarten.de/kartographie/netze/world_globussegmente_012_100mio.jpg

Would appreciate some tips a lot!

best regards