Handi'
I've never worked with one, but have read good things about the .338-06. I'd bet that a light-for-caliber bullet is the only one for whitetails, however, because the velocity is relatively low (for a .338 bullet) and the whitetail itself will not stress that bullet enough to open it up if it's too heavy. Velocity, bullet structure, and target resilience make up the equation for proper bullet selection. That being given, I'd move up to a 225 gr' bullet from this wildcat for black bear and elk. The .338-06 may be 300 to 400 fps slower than the .338 Win' Mag' with 200 grain jacketed bullets -- so you can see that this reduced velocity is a real consideration! Small deer may actually be outside the reasonable use for this caliber........no offense intended.
In my opinion the .30-06 is probably the better caliber for your small deer with 130 gr' bullets and then for handling black bear of any size, and elk to possibly 300 yds.....using 180 gr' projectiles.
Good hunting to you.
SS'