I love this idea!
Have you watched any films (really good one with Michelle Pfieffer that students watch at school) or been to see it performed? This is a great way to get inspiration as it is one of Shakespeare's plays that requires a lot of stylistic input to make the world in the forest real.
You could have a "fairy bower" which could be a swing or seating area draped in vines and flowers.
Flower girls can be given the names of the fairies (or you could name your tables after them).
You could have a special cocktail which can be Puck's love potion and you could display the extract from his soliloquy which describes it.
Perhaps (slightly mad idea) you could ask a few friends to put together the Mechanicals play and this could be part of your evening entertainment! You could play Thisbe and your OH could play Pyramus.
Rather than having Mr and Mrs signs where you'll sit, have Oberon and Titania and you can both be the king and Queen of the fairies.
Lots of fairy lights are a must! and as much greenery as you can manage. I love the idea of an 'overgrown' centrepiece, as though it came from a mysterious forest.
Here is a donkey hea, your OH could wear it for some photos!
I once wanted a wedding in the style of the Emma Thompson film version of Much Ado...A beautiful Italian brick villa with beautiful grounds, everyone wearing white, and an all night part outside!
I hope some of this helps!