Eco-friendly options!

The idea of eco-friendly will probably not help here. You are doing a one-time event so anything you do will be not make a dent for or against the planet. Anything you buy will be added material and even plastic has small chances of actually being recycled.

Pyrex glassware still could break. Pottery or ceramic could break but may not be a concern about the effects of the broken pieces. Those would also be heavier so they wouldn't be caught in the wind normally. Wood cups would be a bit odd but might be useful for holding plastic cups so they are not blown in the wind. Metal cups probably would not work well with the decor -- but are a possibility.

How about renting stainless steel mint julep cups or copper mule cups? I'd get in touch with rental companies for other non-glass options. Rentals use reusable dishware versus disposable paper or wood plates. Plus, all you have to do is stack the dirty dishes, cups and the company will clean up as is. For centerpieces, fresh flowers are biodegradable versus fake. You can even go with potted plants or fruit. Or you can rent non-flower centerpieces or buy and give away these to guests at the end of the night. Good luck.

I think if you do one time use items you could at least look into biodegradable or recycled plastics/paper, etc.