Question about glassware for a tasting party

I’m going to be hosting a tasting for some friends soon, and between the number of people and the number of different whiskies I won’t have enough actual glasses for the event. Ideally people will have access to a fresh glass for each different whisky they try.

So all that said, would using those small, clear disposable plastic cups (like the kind you’d find next to a punch bowl at Christmas) be acceptable? Would they have any adverse impact on the taste of the whiskies? Or should I try to round up enough glass tumblers and just encourage rinsing them between whiskies?

Your advice and feedback is greatly appreciated!