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.
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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...?!?