Alternatively you could always mention it when they RSVP. You could mention they were welcome to bring a bottle if wine if they wanted a drink with their lunch.
I don't find it bogan at all. But then again I used a strider plus and have down lights.
Alcohol is standard at all the 1st birthdays I have been invited to. No one gets wasted. We provided alcohol at both our kids birthdays and their subsequent birthdays we provided a couple of bottles of wine for family to have a drink with cake.
Our friends and families are adults. They know how to drink in moderation. The main focus is still on the children.