2000 chevy express 2500 radiator

ok hopefully someone knows is this is right or not? I am replacing my
radiator in my 2000 chevy express van. when i took the old radiator out, the
transmission lines to the radiator werent connected to anything??? just
hanging there. ok i traced the transmission lines to the front of my van & they
are connected to an auxillary trans oil cooler.... the radiator i bought states: it
"comes with both automatic trans and engine oil coolers"  & it also says
proper fittings for trans lines "if needed"..... ok, so if this is true my van
doesnt need the transmission lines to the radiator correct? because i have
the aux trans oil cooler correct? i can just put my new radiator in & not have
to worry about the trans lines because they are connected already? i'm not a
mechanic but i can do my own work, but this freaked me out just a little, but i
think ive figured it out? any input would be appreciated :-)