Just some quick comments:
Some cars do come without transmission dipsticks. Generally they are the ones that take synthetic ATF and you don't check or add fluid unless there is a problem or it is being serviced.
If that is a fill plug (or port) on the top part of the transmission there really shouldn't be any or much fluid that gets at the underside. So, I'm thinking that if you have the piece that broke off (all one piece? or did it break into 2 or more?) you *might* be able to:
A) Clean the affected area with some carb cleaner (or something that cuts oil and will evaporate quickly). Be sure to take care not to get a ton of it into the transmission through the broken opening.
B) Test fit the broken piece to learn the orientation that it needs to be installed at. Mark it and the case with a Sharpie Marker so that when the epoxy is on it, you'll be able to fit it in the right way. Clean the edges of the piece that broke off, mix up some 2 part epoxy and epoxy the broken piece back onto the case.
C) Let it 'cure' for at least 2 hours (a day would likely be the longest it will take to be fully cured). Run and drive the car with periodic checks to see if any fluid is leaking out.
Being that it is on the top of the case and used as a fill port it likely doesn't see much fluid or any pressure. If that is the case, then just 'gluing' the broken piece back on should do the trick. Please realize that when you are dealing with cast metal that is broken, it looks kind of porous (like you broke a piece of frozen sand apart and looked at it from the side). That is the same reason that if you use a 2-part epoxy to 'glue' the two 'clean' pieces back together they tend to bond really well (again, they can't be covered in oil or grease).
Please remember not to goop a ton of epoxy in there. The trick is to get the minimum amount needed to get the pieces to hold together. Some guys think you need a 1/8" in between the pieces, when in reality, a quarter of that would be more than enough. Of course, this assumes that the broken piece fits nicely together without the use of epoxy in the first place (a clean break of only one or two pieces).