Most cups you can cut off with a knife. Contact the local racetrack tack shop or see if you can order a pair online, there are tons of people who do custom blinkers and it probably wouldn't cost much if you ask for no cups.
Well, you could get customs. Though honestly I've been debating getting a set WITH cups, to dial back the horsey ADD. (Lucky raced in them, though, so the only risk would be him possibly getting a little "up" once they're on. Don't know how a horse who has never worn them would react.)
You can cut the stitching that holds the cups on and remove them completely. It may take a little time to cut multiple stitches but that should do it! GOOD IDEA, by the way. I'm surprised that I don't see more items in tack shops that would help horses be more visible during hunting season. A reflective vest may be great for a rider but what if you get dropped & the horse is running loose through the woods...?!?