With a cheap or second hand spray container such as that used for the garden or the kitchen, stick some 1:1 syrup in and adjust to squirt rather than spray. The spray hole may need to be adjusted to get a proper squirt.
Either measure or weigh ten squirts to determine the amount of syrup delivered on each full pull on the trigger, by dividing the total delivery by ten, to reduce the measuring accuracy.
So it might take as many as five pulls per seam (I can't remember) but it's either cheap at the Pound shop or free if you wash out a kitchen sample.
I saw a couple of years ago, during a cold winter. a dosing gun that wouldn't perform properly because of the viscosity of the syrup. And that was neither free nor cheap.
Not only that, but a lot of the tops on these sprays have a thread that is compatible with a lot of drinks bottles - for a larger reservoir if needed.