What would happen if I changed just the end ball to a different mass (but of the same material, so it would be a different size)? Would it change the conservation of momentum or would it stay the same?
Conservation of momentum is fundamental and has nothing to do with what your ball looks like.
In the usual approximation of Newton's cradle, the masses are taken as point masses, strings weightless and no friction is assumed. In this approximation the size of the balls does not matter (as they are assumed to be points). Furthermore conservation of momentum and kinetic energy (i.e. elastic collisions) are assumed.
What would happen...?
Depending on how you pick the mass of that special ball, all kind of things could happen. For instance one normal ball hitting from one side could make the special ball and another ball move at different speeds on the other side. You can easily do the maths for yourself assuming momentum and energy conservation.
If for instance the special ball has mass equal to twice the mass of the other balls you could have a cradle with only the heavy (special) ball moving on one side and two normal balls on the other. This would be completely equivalent to the regular cradle with two balls moving on each side.