The issue is it might be conflicting with her morals. That's a mental issue on her part which ImO can only be tackled with a lot of explaining and comforting done by the husband. It is
your responsibility to make her feel well no matter if she will go for it or back out.
First of all i don't think it is appropriate to call it "sex outside her marriage" because it is something both of you wish to do or at least to try. It means it has been discussed and agreed upon
inside your marriage and will
extend your marriage and not attack or disparage it. Convincing her of that may help.
i was in a "wifesharing" lifestyle before and our definition of sharing her was quite different. At first she had been worried because of the same reasons you describe but after considering our new lifestyle part of our relationship she was put at ease.
We always considered the following terms...
marital sex = sex with ones marital partner
intramarital sex = sex with anybody who is not ones marital partner but with the partner's consent and approval = sex inside the marriage
extramarital sex = sex outside the marriage = cheating
The point is: If a shared sexual lifestyle is or becomes part of your marriage it can never be cheating! - Make her understand (and feel!) this simple fact.