Yes the 414 should use Hytran or the equivalent in both the loader and the tranny. I use the Premium UTF from Tractor Supply, as long as it meets the Hytran specs it should be fine.
I suspect you tractor uses a common sump in the tranny anyway, my 1968 2444 does.
You will have about 3 drain plugs on the bottom to pull, and possibly one on the rear of the lift box assembly, depending on your configuration.