Yes, I double checked. Your printer is listed. Unfortunately, my eyes aren't what they used to be once upon a time when I was young. 😟
That .exe file is obviously a wIndows file, but here should be an update for the printer for Mac as well. If my eyes are not deceiving me again, I see a printer driver update for Mac here....assuming that I chose the correct printer this time.
http://www.samsung.com/us/support/owners/product/SCX-3405W/XAC
Did you try running Software Update on the Mac? I know that supported printer updates will appear in the Mac Software updates because my HP PhotoSmart 7520 shows updates in there.
The iMac and MBA are seeing the printer so the wireless seems to be working OK, but sometimes rebooting the router can help anyway. But that didn't work for you. I'm not sure what to suggest now. Reinstall the software?
There is an online chat feature on that website that I referenced above. Maybe a chat with the Samsung support people could shed some light on this.