Went to my local AD and they told me that they need the the watch ref and they would need to check with Omega if they could sell me the strap
Is this normal?
No, ADs are hit or miss with anything other than selling you a new watch. There's no part restriction with straps. You should try a Swatch-owned Omega Boutique. You might not even have to visit one... try calling them and they may ship.