Most Helpful Guy
It won't actually make too much of a difference except that the cookies may end up with more or a cake-like quality. If you make sure to knock as much air as possible out of the mixture when rubbing together then you will probably negate most of the rising anyway. As for the salt, shortbread traditionally contained an element of salt anyway so that's no issue.
Most Helpful Girl
I'd suggest finding a different recipe that uses self rising flour. Otherwise you will have to omit whatever rising agent the recipe calls for, but it's hard to know for sure if the ratio will be correct. You might end up with the wrong amount of rising agent.
If you're using salted butter, omit any added salt that is part of the recipe. The amount of salt in the cookies may not be perfect but will probably be okay.