Welcome to my world. We have an acre of what we call an orchard: young fruit trees and rough grass. We have planted some wildflower plugs into one area of it but we battle docks every year.
I do use Grazon, but I don't have a pond. If I was in your situation, I'd use Glyphosate (Roundup or similar) and just make sure that I targeted it very closely on the dock leaves so it didn't kill the surrounding grass. Now is a great time to do it, when the fresh leaves are growing strongly.
If you have a farming supplies shop near you, I'd buy a backpack sprayer and generic glyphosate which you can dilute - it will be much cheaper than garden centre bottles.
Now the bad news: we've been in this house for three years, and I spray for docks every spring. And every summer I wade through the grass looking for any docks I missed and cutting off seed heads (those brownish/red things) and binning them. Docks are very persistant and, when the leaves are small, hard to spot.
For what it's worth, we don't mow the grass short all through the year. Instead we let it grow up until August, allowing time for the wildflowers to flower and set seed. Then we hire a heavy-duty brush-cutting mower (our tractor won't deal with hip-high grass!), push it through the field and rake it up. If you live in the countryside, another option is to ask a local farmer if s/he wants to make hay from the field. If there's nothing else planted in it, they might mow and remove the hay for you.
If you want it to be lawn, then a lawn tractor (although you will probably need to use a brush-cutting mower once just to cut it down to a manageable length) used regularly will help to deal with the docks too, although weedkilling will be necessary alongside: the mower will stop them growing big or setting seed, but it won't kill them.
