No...it would not be weird!! We went and got them from City Hall 2 years ago for the kids as it was their first trip. First thing we did after a photo in front of the train station!
When we went to Toon Town Morning Madness a cast member noticed their buttons and asked them if they were enjoying their first trip etc. He then came back with another cast member who asked them if they would like to help Mickey Mouse and The Mayor do the swearing in ceremony. We were the "Honorary Family" of the day! They gave us the sashes to wear, we went up on stage with the Mayor and Mickey and ALL the characters. They had a cast member take photos with our camera for us.....she took A LOT...and we got a certificate from Mickey and the Mayor to bring home. Priceless family memories all from those "First Visit" buttons!
I WISH we had known about the first trip buttons when DH took me to DLR for the first time! I would've worn one with pride, LOL! Fortunately we learned about them in time for our very first trip as a family when we took our sons two years ago. We stopped at City Hall first thing and picked up the buttons. They wore them every day of our trip! They're just a fun little thing and can garner you (or your children) that extra bit of attention and make your trip that much more magical!
Try to get them first thing in the AM. When we went in July they were all out of them. We weren't able to stop by City Hall in the AM but later in the afternoon after the parade we stopped in and they had NONE! I was totally bummed