Haha notating swing rhythms can be complex. It is mostly about learning conventions to get the sound you want out of musicians who already read in the style. Example: a jazz musician reading a dance band chart will always play a quarter note short if it is followed by a rest, unless otherwise notated. Why? My theory is that it was physically easier for copyists and arrangers to write. Also jazz is traditionally written with twice a many bars as pop music or classical music. I've heard that somebody at some point was getting paid by the measure for arrangements and found an easy way to double their fee, but that may just be a joke. Everything has a nickname too: fermatas are birdseyes, caesuras are train tracks, etc. There is a somewhat standardized system for marking up charts as well, but I never learned it. I do remember that circling a bar or group of bars means skip the circled section entirely. That sort of thing. It makes sense to have a standard way to do it, so that any musician can pick up the same chart with the same pencil revisions and play it the same way. If neither the musicians nor the arranger are familiar with the conventions of swing notation the experience will likely be frustrating. Good luck!