I would disagree with the use without IS. When you are shooting wildlife you are probably shooting fast enough to make IS void.
70-300mm L is a really nice lens. The 400 F5.6 is probably the best bang for buck. More important is the understanding of the animal you are shooting.
No no no no no! Noooooo. IS is so important for wildlife. Many many great wildlife activity and sightings happen in low light and IS is paramount in those situations…. Not all wildlife photos are hunting cheetahs! And it gets worse in ever green forests like India and Costa Rica…