Yeah, there are always those things to consider.
I believe that so long as the projectile has a strong jacket to start with, and the reduction is no more than about 5 thou max you should not have any problems.
Bear in mind that the standard bullet cops a quite savage and very fast swaging in the rifling when the gun is fired and usually they don't have any problem.

I have though had problems keeping the ogive concentric to the bullet shank, if the reduction is more than 5 thou. (on the smaller calibers anyway)
At one stage I made a die to reduce 9.3mm (.366") down to .358 all in one operation and found this to be a bit too savage and had trouble with concentricity.
Maybe a 2 stage reduction might have helped but I didn't try it.
That said, I would be confident that good quality .416's could be reduced to .411 without any bullet jacket damage.

You could always test them on non dangerous game before taking on anything too serious.