Hi Adriane,
That is a pretty large raster; about 63% of the earths circumference... I'm kinda curious; what type of raster data is this, how large is it (several TBs?), and more importantly why do you want to do this?
In general it is a lot easier to project the vector data (shapefile) to the projected coordinate system van the raster. If you project a raster you will probably apply some resampling and create a second dataset (which, depending of the cell size, will probably be huge too).
Kind regards,
Xander