All parts of the ac circuit get dirty - which is why you need to clean them.
Removing the evaporator will not remove all the smell and will stop the ac working.
The ac can be used to demist the screen in many conditions - a task that used to happen before ac was so common by blowing air or using wipes.
Two things you can do (which I can think of) to eliminate the transmission as the culprit:
When you pull the dipstick, if you smell the transmission fluid and it doesn't smell burnt (there's a DISTINCT difference when it is burnt) and is a nice cherry color as you've already stated, it should be in good shape.
On the radiator, there are two small hard lines ...