Was there a reason for management to impose these restrictions on you?
I see no operational or safety argument, which would make shift swapping a bad idea.
I work TWR/APP in Copenhagen, Denmark. Our rota is 4 on 2 off. No more than 10 working days in a row.
Just had a look at my May rota. I've swapped 13 shifts this month alone. Some to help myself, some to help my colleagues.
I'm having a hard time seeing anything wrong with this.
/MorfArsenal