Here's an example of a MB-Momo horn button, and yes they have dual contacts.
https://www.ebay.com/itm/MOMO-MERCEDES-BENZ-HORN-BUTTON-AMG-STEERING-WHEEL-W123-W124-W126-W115-W114-R107/173719328923?hash=item28727a989b:g:2pwAAOSwR2RaCGAb
Can sometimes find them a bit cheaper. I bought and sold one because the Momo OD is a little smaller than Nardi horn button ID, so there was a gap and couldn't use the trim ring. Then later I lucked out and found the MB-Personal horn button in the above photo.
I've seen some stick-on adhesive wheel center caps that might work with the horn button on that steering wheel you bought. Take some measurement when you get it and eventually you'll find something to spiff it up.
There are also off-brand horn buttons with MB logos. Many of them are made using single contact horn buttons, so just be sure to verify with the seller if you go to purchase one.
https://www.ebay.com/itm/Mercedes-Benz-Badge-Horn-Button-Fits-MOMO-RAID-SPARCO-NRG-Steering-wheel/163332375359?hash=item26075e433f:g:9QAAAOSwa6Zbq8oZ