Missing the point here I think chaps...
He's asking if he should do anything
different, not do less. i.e. will following his cleaning routine for a blue rifle damage a stainless one.
0423socket, assuming I've got that right then no there isn't anything different you need to do.
If it's second hand...
Patch out any oil in case there is too much in there.
Patch with some copper solvent and scrub it out with a nylon brush to remove any residue.
Patch in a new thin layer of oil to protect it until you're ready to shoot (patch out the oil so you have a dry barrel before shooting)
If it's new...
There won't be any copper from firing so no need for solvent.
There will be tonnes of grease in the barrel from the manufacturer - patch it out good!
Once you've given it a good patch and scrub and you've got a nice shiny new barrel interior oil it until you're ready to shoot as above.
Hopefully I haven't assumed incorrectly there and just explained a whole bunch of crap you weren't looking for