The 404 would be fine and a moderate recoiling bolt action rifle. You may also wish to consider getting a 416 Remington and have Superior Ammo or other custom ammo makers make some reduced pressure rounds.

A 416 should be much cheaper to find that the 404 and as stated above others can download it for less recoil. The total cost of such a rig may be less than a 404 bolt.The upside is that if the reduced loads are not enough then you can just buy some factory stuff at full bore!!

Just a thought--