Aha! Thanks so much for that, i'll have to remember it for the future.
I was previously trying to search for a file that the launcher would store the parameters in, but I didn't know where to look and exporting the launcher logs only shows the name of the parameters used during the last launch, but not the values.
So the solution worked and what I managed to find out is that the unit parameters works by passing a series of numbers to the game. In my case it was
-unit=4881
Which is for the Unit Z Special Unit
That then creates another problem though in how one would actually find the number for their unit, as having to use the task manager to look at the command line isn't ideal by any means.
When looking at the Units website for Arma 3 I seem to have just happened to stumble on a soloton though. While it may not be the correct way it's simple enough to do which is good enough for me!
So the process is, when logged in to the https://units.arma3.com/my-units page it will list up to three units you are currently in (with 3 being the limit). When you click one of the big black boxes to select one of the unites, it expands to show more information but what's more important here is how the URL will also change to https://units.arma3.com/my-units#?unit=4881, where that number at the end is the one we need.
Thanks a lot @Dedmen for taking the time to respond to my topic and giving me the little extra help I needed in order to figure this out. If it wasn't for you then I likely would have just given up on it for not being that important.