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The University of Rochester has an interfaith chapel, but that's obviously not Webster.
The Webster Arboretum is very close to the WGC (it's on Schlegel Road), you may be able to have an outdoor wedding there, but you'd probably have to be responsible for renting chairs. There wouldn't be a very good bad-weather option unless you also rented a tent to be safe. I hear the small building there is being renovated now but will be done later this year. If you're interested in an outdoor ceremony, it is worth looking into.

you should definitely check out the Webster arboretum... it is outside and books early but if it works out for your date you can bring in your own officiant and do what you want with the place. It is decent price too, comparable to getting a church

For an outdoor ceremony there are several places along Lake Ontario in Webster that would be great for a ceremony - see Webster Park for some of the locations. There is also the Webster House Bed and Breakfast - which gives you and your wedding party a great place to get ready prior to the ceremony.
Can you have the ceremony at the Golf Club? That would make things so much easier on you and your guests to not have to travel to another locations...?