You're right in not considering the cladding for stiffness purposes. Its effects will be minimal.

However, the weight of the cladding must be properly considered. You do not want to average the densities of the carbon steel pipe and the alloy cladding. Instead, you want to compute an equivalent density for the pipe material such that the unit weight computed by the software is equal to the sum of the unit weights of the pipe plus cladding.

As to the issue of whether or not the cladding will add additional load on your nozzle, I don't think so. You're considering the proper weight (via the equivalent density), and any other system loads encountered (through system displacement) will affect the nozzle regardless of the presence of the cladding.

Perhaps others have additional insight into this problem?