The vibration may not be a big issue, I am only basing it upon my sprayer experience. I think the nozzles cap would tend to vibrate loose but could be wrong. However based upon my limited experience of spraying row crops and hay fields and such, often 20 inches is as near as nozzles are recommended to what is being sprayed and one reason is to give them distance to allow the spray to open up to the needed width. Then I certain don't know all the different types of nozzles and their specs. It certainly would not be hard to install a bar on the cutter to mount nozzles. Maybe boomless nozzles would work. Would be my recommendation.
Will you be mounting tank on the front of the tractor or a saddle mount off one side? Front end probably would give better balance. Depending on what you are mowing many need to protect the tank and any hoses.