If you decide to spray there are a few things to consider.
Here's one of those "things."
Are you required to have an applicator's license in your area? Check with your local extension office. Penalties in some areas for applying any type of chemical (yes, even round-up) for a commercial purpose without proper licensure can result in fines and other actions. That might sound overly paranoid but better check just in case.
For spraying, use as narrow a nozzle as possible to reduce over spray and nasty brown strips several inches from the fence. Don't over mix your chemicals. Mixing to a stronger concentration normally doesn't kill grass any better and it just wastes money.
For trimming, use as heavy guage line as your trimmer will handle and run your trimmer at a lower rpm than during normal use. This will reduce the amount of line used and will reduce the number of times you have to rewind jamed-up line.
Good luck. Chainlink = Blah!